The Local Incidence of Trade Shocks Ferdinando Monte Georgetown University This version: March 17, 2016
Abstract The welfare implications of trade integration across areas of a country rely on local real wages, typically unmeasured in ex-post analyses and unavailable in counterfactual exercises. I develop and estimate a general equilibrium framework where local labor markets interact via commuting ties and overlaps in sectoral specialization. Changes in real wages are poorly predicted by standard measures of exposure to trade because, …rst, the price of local services co-moves with local workplace wages, and, second, residents adjust commuting patterns chasing higher wages. While more exposure to trade in comparative disadvantage sectors tends to lower nominal wages, all real wages grow. The two margins of adjustment are empirically active: in a standard di¤erencein-di¤erence analysis for the United States, the share of a locality’s residents working there, median rents and housing prices decline faster in places more exposed to increases in import competition from China.
McDonough School of Business. Email:
[email protected]. I would like to thank Costas Arkolakis, David Atkin, Luigi Balletta, Federico Bandi, Mark Bils, Lorenzo Caliendo, Thomas Chaney, Alan Deardor¤, Peter Debeare, Rafael Dix-Carneiro, Steven Durlauf, Ron Jones, Sam Kortum, John McLaren, Angelo Mele, Dan Lu, Esteban Rossi-Hansberg, Pete Schott, Bob Staiger, and seminar participants at 2013 Midwest International Trade Meetings, 2013 EIIT, University of Rochester, USITC, Darden School of Business, Princeton, Yale, Georgetown, Philadelphia FED, 2014 Econometric Society Summer Meetings, 2014 TIGN at Universidad del Chile, Richmond FED and UC Davis for very helpful discussions. Kadee Russ provided very detailed comments on the …rst draft of this paper. Early funding from the National Science Foundation, Doctoral Dissertation Research Grant #0962616 (2010), is gratefully acknowledged. All errors remain my own.
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1
Introduction
The consequences of international integration are heterogeneous in space. Di¤erent places tend to be specialized only in a subset of tradeable sectors, and sectors have varying degree of concentration across locations. Hence, reduction in transportation costs, trade agreements, trade rebalancing, or foreign productivity growth have di¤erential e¤ects over the territory of a country. Several studies have indeed documented this heterogeneity in the incidence of international integration, and concern has grown that trade may impact adversely some areas particularly exposed to import competition1 . Importantly, while changes in real wages would be the ideal measure for welfare analysis, they are typically unobserved at the local level for ex-post studies, and are of course unavailable in the evaluation of new policy proposals; when looking at wages, the empirical literature has then been constrained to analyze changes in nominal wages, at most corrected for economy-wide changes in prices. To assess the ex-post welfare consequences across space of integration episodes, and even more to evaluate new policy proposals, one needs a way to generate changes in real wages in a world where local labor markets interact with each other. In this paper I use a general equilibrium, open economy model to assess the local real wage consequences of a trade liberalization. I …nd that typical exposure measures based on local sectoral employment shares predict well nominal changes in wages, but have a poor predictive power of the incidence of trade on real wages across locations. Both in a one-sector liberalization and in an “autarky-to-current trade frictions” exercise for the U.S. economy, locations more exposed to trade do experience stronger changes in nominal wages of workers employed in those locations and of residents living there; however, exposure to trade has almost no predictive ability once I consider model-generated real wages. Consistently with empirical …ndings, liberalization impacts negatively nominal wages in locations more active in comparative-disadvantage sectors; yet, all locations gain from trade in real terms. The link between exposure to trade and real wages is almost completely severed for two reasons: …rst, when workplace wages decrease, the price of local services for residents (e.g., rents) also decrease, and non-tradeable goods and services account for a large share of expenditure; second, residents can always chase relatively higher wages by changing commuting patterns and sectors in response to possibly adverse shocks. On the other hand, trade 1
See for example Topalova, 2005, or Autor, Dorn, and Hanson, 2013, among others.
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still bene…ts consumers through standard comparative advantage arguments. I show, to the extent possible, that these two mechanisms do respond to increases in import penetration in the expected way: in a typical di¤erence-in-di¤erence analysis, localities more exposed to increases in Chinese import penetration in U.S. experience a faster decline in the share of residents working in the same locality, in median rents, and in housing prices. I further show how locations inactive in a sector (which would then have no exposure to the policy under standard measures used in the literature) can nonetheless be impacted by a liberalization in that sector. I …nd that there is basically no di¤erence between locations active and those inactive in the sector being liberalized, both in the distribution of changes in workplace nominal wages and in that of real residence wages. I am also able to determine that a majority (around 60%) of the equilibrium change in nominal workplace wages comes from equilibrium interactions with neighboring locations, i.e. local labor supply and demand linkages generate strong spillovers. On average, only 8% of the total change in nominal workplace wages of active locations is attributable to direct exposure to trade. The importance of local interactions is also evident once I compare these wage predictions to what one would obtain under the assumption of no commuting ties between locations: we would overpredict wage changes in locations active in the sector and underpredict those in inactive ones. In the theory, the world has a home economy and a foreign economy. While the Rest-of-the-World (RoW) is modeled as a single-location with many sectors, the home economy is a set of locations where people live and produce in several sectors. Agents (exogenously) reside in distinct locations and they can work either where they live or in neighboring places within commuting distance. Residents in a location are always arbitraging between wages paid in any pair of possible commuting destinations: hence, changes in the prevailing wage in the two-neighborhood of a location (not only its neighborhood) can impact labor supply to this location directly, and absence of commuting ‡ows does not imply absence of labor supply linkages between labor markets. I say that two labor markets are connected when they belong to the twoneighborhood of each other2 (and call all the others unconnected labor markets). Heterogeneity in idiosyncratic workers’preferences regulates the sensitivity of labor supply to a location with respect to local wage di¤erentials. The production side 2
When the notation is laid out below, a more precise de…nition accounting for the possibility of one-way commuting only will be given.
3
follows the framework proposed by Eaton and Kortum (2002), where I assume no internal transportation costs. A subset of industries is (exogenously) active in any location. A location’s wage a¤ects another location’s local labor demand if they are active in a common subset of sectors. Heterogeneity in idiosyncratic varieties’ productivities (i.e., the strength of comparative advantage) regulates the sensitivity of labor demand across sector-locations to prevailing wages across locations. Crucially, a locally produced and consumed service generates residence-speci…c price indices. After describing the equilibrium properties of the model, I separate theoretically the di¤erent components of the equilibrium adjustment of a location’s wage to a shock in a 1) direct e¤ect, indirect e¤ects from 2) connected and 3) unconnected labor markets, and 4) trade balance adjustment. The framework is general enough to deal with the transmission of shocks to any parameter of the model and could be used to study technology improvements at home and abroad, investments in transportation infrastructure, or immigration episodes, in addition to the consequences of international integration. The model is also ‡exible enough to incorporate realistic geographic features such as the set of observed commuting ties among locations and the active sectors throughout the U.S. economy. I focus on a world economy made up of the United States and RoW. I estimate the job location choice parameters with data on commuting patterns among 1,230 Public Use Microdata Areas (PUMAs), covering the entire continental United States, and …nd that transportation infrastructure is very important in raising the elasticity of relative commuting ‡ows. I estimate technology parameters using PUMAs employment by location and industry and standard international trade data by sector, and …nd that the strength of comparative advantage is similar in range to values already commonly used in the international trade literature. The contribution of each component of the transmission mechanism can be then computed in principle for any counterfactual exercise, and full general equilibrium exercises can be carried out. The geographic incidence of trade shocks is the subject of a recent new stream of research, of which this paper is part. Several studies3 have documented empirically the e¤ect of international trade integration on within-country geographical units by 3
See Hanson, 2005 and Chiquiar, 2008 for Mexico, Topalova (2005, 2007, 2010), Hasan, Mitra, and Ural, 2006 and Hasan, Mitra, Ranjan, and Ahsan, 2012 for India, McLaren and Hakobyan, 2010, and Autor Dorn and Hanson, 2013 for U.S., McCaig, 2011 for Vietnam, Kovak, 2013 for Brazil. Early work across U.S. metropolitan areas by Borjas and Ramey, 1995 is an important precursor in this literature.
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relating changes in exposure to international competition to changes in local outcomes such as the incidence of poverty, unemployment, wages, and the take-up of federal bene…ts. The paper contributes to this literature with a theoretical framework which decomposes the propagation mechanism in meaningful terms emerging from commuting ties and overlaps in sectoral activity. My …ndings imply that geography has an independent role in the propagation, and measures of exposure to trade only based on the share of employment in sectors impacted by liberalization may not be adequate to speak to the real wage consequences of trade. Importantly, I also show that the level e¤ect of trade, unidenti…ed in di¤erence-in-di¤erence exercises, is positive: trade does have a heterogeneous incidence over space, but in a context of ubiquitous growth in real wages. The literature has analyzed geographical units of varying size4 . The model indicates that having larger units of analysis may not be enough to exclude linkages between locations: the absence of commuting ‡ows between two areas is not su¢ cient to sever their labor markets, and, for given distances, small commuting ‡ows are indeed those who carry with them the highest potential for transmission, as they raise elasticities of labor supply5 . The literature on labor mobility typically argues that internal migration of labor is slow and only partial6 . To some extent, the results in this paper point to alternative margins of adjustment that make internal migration less necessary in response to a shock. The results in the present paper are based on a medium-to-long run perspective, where the distribution of employment across locations and industries is allowed to change, trade is allowed to rebalance, while the distribution of residents and industries’location and the network of commuting possibilities is kept …xed. The assumptions on labor mobility in this paper fall then mid-way between immobile labor across locations (e.g., Kovak, 2013) and perfectly mobile labor across locations (e.g., 4
Topalova, 2005 focuses on Indian districts; in U.S., Autor, Dorn and Hanson, 2013 use commuting zones, McLaren and Hakobyan, 2010 study consistent PUMAs; Hanson, 2005 and Chiquiar, 2008 consider Mexican regions. 5 Moreover, larger units may partially mitigate the need to account for interactions, but not to measure accurately real wages, and they come at the expense of distancing the analysis from a meaningfully local dimension. 6 See for example Topel, 1986, Blanchard and Katz, 1992 Glaeser and Gyourko, 2005, Kennan and Walker, 2011 and Notowidigdo, 2013. Consistent with this evidence, Autor, Dorn and Hanson, 2013 show that within the two decades time frame they analyze there is only limited internal migration of workers across areas in response to demand shocks; Topalova, 2010 also …nds no role empirically for workers’ migration response among Indian districts. These facts give empirical justi…cation to the assumption of a …xed distribution of residents and are consistent with the identi…cation strategy of the model.
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Caliendo, Parro, Rossi-Hansberg and Sartre, 2014).7 To the extent that internal migration matters empirically more than allowed here, one can see this paper as showing how much commuting ties matter alone in spreading a shock over the territory of a country. This paper is also similar in spirit to Caliendo et al. 2014, who study the e¤ects of changes in technology in a state-sector on all other states in the United States, assuming perfect labor mobility and an explicit role for input-output tables and internal transportation costs. Here, I ignore input-output relations across industries, but allow for commuting and an open economy environment.8 Other studies o¤er structural models of labor markets, and characterize the dynamic adjustment to changes in the international environment.9 This paper assumes free job mobility across sectors and locations (up to individual heterogeneity), no internal migration, and only compares steady states, but can focus sharply on the consequences of commuting and intersectoral concentration. This focus allows us to study local mechanisms of transmission, and to depart from the common small open economy assumption to highlight the role of rebalancing of trade on the equilibrium change in wages. This paper delivers a gravity structure for commuting ‡ows similar to Ahlfeldt, Redding, Sturm and Wolf, 2012, who develop a quantitative theoretical model of city structure and use exogenous variation induced by the rise and fall of Berlin’s Wall to identify the role of agglomeration and dispersion forces and fundamentals in location choices. While the data available here is at a more aggregated level, I show that the observed network of commuting ties can have deep implications on (and promising applications for) more macro-level issues, like the impact of immigration, technology or trade shocks in general equilibrium analysis. 7
Kovak, 2013 is a speci…c factor model where workers are speci…c to locations, while in Caliendo et. al, 2014, workers are not attached to any geographical unit. The present paper may be viewed as a case of the speci…c factor model where labor is speci…c to a group of locations, and di¤erent location can use di¤erent, but overlapping, groups of factors. 8 Other papers highlighting the importance of input-output matrices in open economy are Caliendo and Parro 2014, and Ossa, 2013. A recent stream of literature (Allen and Arkolakis, 2014, Cosar and Fajgelbaum, 2013, Donaldson (forthcoming), Donaldson and Atkin, 2013, Donaldson and Hornbeck, 2013) studies more generally the role of within country geography on heterogeneity in local economic outcomes; none of these contributions addresses the incidence of trade shocks in a local labor market setting, or studies the relation between exposure measures and real wages. 9 Contributions by Artuç, Chaudhuri and McLaren, 2010, Artuç and McLaren, 2012, Cosar, 2013, and Dix-Carneiro, 2014, show how to study transitional dynamics of trade shocks, integrating to varying degrees industry-speci…c and occupational speci…c-labor mobility costs.
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The rest of the paper is organized as follows. Section 2 provides empirical evidence on the importance of adjustment in commuting and local prices. Section 3 sets up the model and establishes properties of the equilibrium. Section 4 studies theoretically the propagation of shocks. After describing some of the main characteristics of the data in Section 5, I show how to identify and estimate the main components of the model in Section 6. Section 7 uses these estimates in two counterfactual exercises. Section 8 concludes emphasizing important limitations and possible directions for future research.
2
Reduced-form evidence
In this section, I provide reduced-form evidence on the response of commuting and local prices to trade shocks following the framework proposed in Autor, Dorn, and Hanson (2013). As a reminder, their di¤erence-in-di¤erence estimation compares the response of an outcome d ln yi;t across di¤erentially exposed locations over time (us)
d ln yi;t = c +
IP Wi;t + "i;t
(1)
The exposure measure is a contemporaneous locally weighted average of increases in U.S. imports per worker (us) IP Wi;t
=
X L(s) i;t s
Li;t
(s)
M(us);t (s)
Lt
(2)
and to limit endogeneity problems, such a measure is instrumented with 10 years lagged, locally weighted average of increase in other developed countries imports per worker (s) X L(s) M(oth);t i;t 1 (oth) IP Wi;t = (3) (s) L i;t 1 L t 1 s I extend the analysis in Autor, Dorn and Hanson (2013) to examine the response of commuting and local prices to the same trade shock. I examine responses both at county level and at commuting-zone levels. In each case I repeat the estimation twice: I …rst estimate the 2SLS with the exposure in levels (as it is indicated by the formula, to maintain comparability) and then use exposure (and its instrument) in logs, which are my preferred estimated, especially at county level, as they result in a better …rst 7
stage. As a measure of commuting, I use the change in the share of residents in a locality who work in the same locality. This measure is arguably the most (directly) impacted by the shock to a given locality, and so it provides a relatively clean outcome variable: the change in the share of residents of a locality i0 commuting to the impacted locality i would depend (to a larger degree) on the intensity of the shock in i0 and around it, as well. It is also a measure that summarizes well the heterogeneity in elasticities of local employments to local shocks (Monte, Redding, and Rossi-Hansberg (2015)). Measures of local prices are notoriously di¢ cult to obtain, especially for small geographic units and far back in time. To the best of my knowledge, median county rents (from U.S. Census) are the only local prices available going back to 1990. Note that this is a somewhat imprecise measure, since it does not control for house characteristics or family size. As a robustness, I also provide partial evidence on the response of housing prices for a subsample of localities and a shorter time period, as reported on a widely used real estate website10 . Table (1) shows the coe¢ cient in regression (1). The right-hand side exposure has been normalized to express the movement from the 10th to the 90th percentile of exposure. Over the whole sample, higher import penetration causes the share of residents working in a county to drop by 2.6 percent over 10 years. Of course this is not the full impact on commuting, since commuting ‡ows are reshu- ed among all counties in a way that depends on the correlation of the trade shock across neighboring counties and on the initial commuting probabilities11 . The results however show that reshu- ing in commuting ‡ows is an active margin of adjustment. Moving from the the 10th to the 90th percentile of exposure also causes the median county rent to drop by (or grow more slowly of) 6.8% over 10 years: to the extent that local economic activity slows down due to relative reductions in labor demand, local prices fall too. Interestingly, looking across sub-samples, we …nd that in periods where the commuting response is stronger, the local price response is weaker: commuting and local prices appear to be substitute mechanisms for smoothing the negative consequences of a trade shock. One may think that aggregating the analysis at commuting zone level will mute 10
I use the median Home Value per Square Foot from Zillow Research. As we will see below, the elasticity of commuting ‡ows to wages depend on the initial commuting composition. 11
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Table 1: Import Penetration, Commuting and Local Prices: County-Level Analysis Only 1990-2000 1 2 log share of residents working in home county (Log) (000 USD)
Dependent variable: (Instrument) (
imports p.w. (U.S.), log)/(p90
p10 )
-0.027*
imports p.w. (U.S.), 000 USD)/(p90
p10 ) 2,989
N
4
log median county rent (Log) (000 USD) -0.025
(0.015)
(
3
(0.030)
-0.030***
0.002
(0.009)
(0.014)
3,108
2,989
3,108
3
4
Only 2000-2007 1 2 log share of residents working in home county (Log) (000 USD)
Dependent variable: (Instrument) (
imports p.w. (U.S.), log)/(p90
p10 )
-0.024**
-0.101***
(0.010)
(
imports p.w. (U.S.), 000 USD)/(p90
p10 ) 2,950
N
log median county rent (Log) (000 USD) (0.029)
-0.021***
-0.059*
(0.006)
(0.031)
3,108
2,950
3,107
3
4
All sample 1 2 log share of residents working in home county (Log) (000 USD)
Dependent variable: (Instrument) ( (
imports p.w. (U.S.), log)/(p90
p10 )
imports p.w. (U.S.), 000 USD)/(p90
log median county rent (Log) (000 USD)
-0.026**
-0.068***
(0.011)
(0.018)
p10 )
-0.022***
-0.038*
(0.005)
N
5,939
6,216
(0.021)
5,939
6,215
* p<0.1; ** p<0.05; *** p<0.01. The "All sample" regression includes a decade …xed-e¤ect.
all the adjustment on the commuting margin. However, Table (2) shows that this is not the case. While the coe¢ cients on the commuting measure are weaker to some extent (commuting zones must capture some commuting, after all) the results show that the commuting margin is active even in this case. Interestingly, the response on local rents is even stronger, indicating that local prices drop more in more populated places within the commuting zone. Again, commuting and local prices behave as substitute mechanisms for smoothing the negative consequences of trade.
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Table 2: Import Penetration, Commuting and Local Prices: County-Level Analysis Only 1990-2000 1 2 log share of residents working in the home commuting zone (Log) (000 USD)
Dependent variable: (Instrument) ( (
imports p.w. (U.S.), log)/(p90
p10 )
imports p.w. (U.S.), 000 USD)/(p90
3
4 log median commuting zone rent (Log) (000 USD)
-0.019***
-0.042
(0.007)
(0.043)
p10 )
-0.019***
-0.025
(0.005)
709
N
722
(0.024)
709
722
Only 2000-2007 1 2 log share of residents working in the home commuting zone (Log) (000 USD)
Dependent variable: (Instrument) ( (
imports p.w. (U.S.), log)/(p90
p10 )
imports p.w. (U.S.), 000 USD)/(p90
4 log median commuting zone rent (Log) (000 USD)
-0.013**
-0.138***
(0.006)
(0.040)
p10 ) 704
N
3
-0.010*
-0.092***
(0.005)
(0.032)
722
704
722
All sample 1 2 log share of residents working in the home commuting zone (Log) (000 USD)
Dependent variable: (Instrument) (
imports p.w. (U.S.), log)/(p90
p10 )
-0.017***
N
imports p.w. (U.S.), 000 USD)/(p90
p10 ) 1,413
4 log median commuting zone rent (Log) (000 USD) -0.097***
(0.006)
(
3
(0.024)
-0.012**
-0.069***
(0.005)
(0.022)
1,444
1,413
1,444
* p<0.1; ** p<0.05; *** p<0.01. The "All Sample" regressions include a decade …xed-e¤ect.
Table (3) corroborates the results on median county rents by looking at housing prices per square foot. The data is unfortunately only available for a subset of U.S. counties, and a comparable analysis can only be conducted for the years 2000-2007. Nonetheless, the results are consistent with changes in rents, and suggest that stronger import competition, to the extent that reduces local economic activity capitalizes its e¤ects in local asset prices.
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Table 3: Import Penetration and Housing Prices County-level analysis: years 2000-2007 1
2 log change in house price per sqft. in the county (Log) (000 USD)
Dependent variable: (Instrument) (
imports p.w. (U.S.), log)/(p90
p10 )
(
imports p.w. (U.S.), 000 USD)/(p90
-0.337*** (0.079)
p10 )
-0.233*** (0.059)
1,011
N
1,021
Commuting zone level analysis: years 2000-2007 1 2 log change in house price per sqft. in the commuting zone (Log) (000 USD)
Dependent variable: (Instrument) (
imports p.w. (U.S.), log)/(p90
p10 )
-0.410***
imports p.w. (U.S.), 000 USD)/(p90
4 Within-c.z. avg. log house price per sqft. in the county (Log) (000 USD) -0.406***
(0.121)
(
3
(0.122)
p10 )
-0.301***
-0.298***
(0.100)
355
N
356
(0.100)
355
356
* p<0.1; ** p<0.05; *** p<0.01
3 3.1
Model Setup and individual behavior
The world economy is comprised by two large countries, Home and Rest of the World (RoW). The Home economy is comprised by a set R of locations. Each r 2 R is inhabited by an exogenous number of Hr agents; the total population in the economy P is H = r2R Hr . These agents choose a job location and allocate their income across varieties produced in several sectors (which I describe below). Each worker provides 1 e¢ ciency unit of labor. An individual living in r 2 R can only hold a job in (i.e., commute to) a set of neighboring locations J (r) R which are close enough. I do not impose a priori restrictions on the sets fJ (r)gr2R , as the structure of these sets can be reconstructed from the data on commuting patterns12 . Since in general J (r) 6= R and J (r) 6= J (r0 ) if r0 6= r, the local labor supply is nontrivial. I assume that workers di¤er from each other in their idiosyncratic valuations of jobs in di¤erent locations: each worker living in r is characterized by a random 12
In particular, j 2 J (r) if (and only if) we see at least one worker going from r to j. The collection of sets fJ (r)gr2R is taken as a technological constraint.
11
vector e = r ~ , i.i.d. across agents and locations, j j2J (r) with Fr ( ) = exp where r > 0 and ~ is the Euler’s constant13 . I assume the utility of choice j for an agent j j2J (r) to be ln wj = (pr drj ) + j , where wj is the prevailing wage paid in location j (and his expenditure), pr is the price index prevailing in location r, and drj 1 is the reduction in utility in terms coming from a two-way commuting from r to j: A worker living in r takes as given J (r) and fdrj ; wj gj2J (r) , and solves Ur ( )
max ln wj = (pr drj ) +
j2J (r)
j
(4)
The foreign economy is summarized by one location, where H agents live and work. I denote with w their wage (and in general use a subscript asterisk to denote the RoW’s economy attributes). Each location in the Home economy is characterized by a local labor supply and a local labor demand which respond to its wage as well wages in other locations: these interactions provide the foundations for the propagation of shocks. In the remainder of the section, I will describe local labor supply and demand, emphasizing their response to wages elsewhere in partial equilibrium; I will then show how all wage changes are made mutually consistent in general equilibrium and the structure of transmission.
3.2
Commuting ‡ows and local labor supply
The solution to (4) implies that the fraction of individuals living in r and commuting to j is (wj =drj )1= r (5) mrj = P 1= r j 0 2J (r) (wj 0 =drj 0 )
Everything else equal, the fraction of residents in r commuting to j increases when fewer alternative options are available to residents of r (i.e., the lower the cardinality of J (r)), and when the commuting costs to j are lower, or the commuting costs to alternative destinations j 0 6= j are larger. Note that mrj is a function of all the wages fwj gj2J (r) paid in all feasible destinations. Since the total commuting ‡ow from r to j is Hr mrj , the local labor supply to any 13
Hence, E ( ) = 0 and V ar ( ) = 2 2r =6: With homogeneous locations, one would ideally restrict all r to be the same. However, since in the data geographic areas have heterogeneous size and di¤erent degrees of transportation infrastructure, I will allow r to be di¤erent.
12
market j is given by L (j) =
X
Hr mrj =
r:j2J (r)
X
r:j2J (r)
Hr P
(wj =drj )1= j 0 2J (r)
r
(wj 0 =drj 0 )1=
r
(6)
The local labor supply to market j is then a function of [r:j2J (r) fwj gj2J (r) , the union, over all residences r that can send workers to j, of all the wages that residents in these r consider when evaluating j. Hence, this set includes also wages paid in locations that do not send workers to j directly, but are in competition with j for workers living in r: even with no direct commuting ties between two locations j and j 0 , wj 0 can still impact labor supply to j directly (i.e., before general equilibrium e¤ects), as workers in some r are arbitraging between these two locations. To understand the response of L (j) to changes in a generic wj 0 , we need to …rst study the response of the fraction of commuters from r to j. From (5), the elasticity of mrj to wj 0 is
" (mrj ; wj 0 )
wj 0 @mrj mrj @wj 0
8 > < (1 mrj ) = = mrj 0 = r > : 0
r
if j 0 = j if j 0 2 J (r) ; j 0 6= j if j 0 62 J (r)
(7)
where " (a; b) will from now on indicate the elasticity of a to b. When the wage prevailing in j 0 increases, the fraction of commuters from r to j may be impacted in one of three ways. If j 0 = j, the fraction of workers commuting to j increases as wj grows, with elasticity (1 mrj ) = r : when j is already very popular among these residents, most of the workers have already selected it, and only those for whom j is very unattractive remain to be convinced: the elasticity is then low14 . The fraction of workers going to any other destination j 0 6= j decreases as wj 0 grows, with elasticity mrj = r : when j is already very popular among these residents, also those for which j is relatively unattractive have selected it, and they only need a small increase in wj0 to be selected away15 . Finally, there is obviously no direct e¤ect on mrj when j 0 62 J (r), as wj 0 does not a¤ect any choice margin. 14
Given (5), mrj is then very elastic to wj if r has many alternative options, is very close to other areas, or is relatively far from j. 15 Hence, mrj is very elastic to wj 0 when r has only a few other alternative options, is very far from other areas, or is relatively close to j.
13
A crucial role in these elasticities is played by r . Formally, r measures the variance in the individual heterogeneity , and thus regulates the sensitivity of commuting ‡ows to di¤erences in wages: when r is large, individual heterogeneity is all that matters and commuting ‡ows do not respond to changes in wages; when r ! 0; all residents in r choose the highest-paying location only.16 Using (7), the elasticity of the labor supply to location j with respect to the wage in j 0 is
" (L (j) ; wj 0 )
8 P Hr mrj > mrj ) = > r:j2J (r) L(j) (1 < P Hr mrj fr:j;j 0 2J (r)g L(j) mrj 0 = > > : 0
r r
if j 0 = j if j 0 2 J 2 (j) ; j 0 6= j
(8)
if j 0 2 = J 2 (j)
where J 2 (j) [r:j2J (r) J (r) is the union, over all residences which can send workers to j, of all their possible destinations, i.e., the set of all job locations whose prevailing wages can directly a¤ect the labor supply in j.17 I say that j 0 is connected to j if j 0 2 J 2 (j), and de…ne J 2 (j) as the local labor market of j.18 Total labor supply to j responds to changes in wj 0 in one of three ways. The elasticity of L (j) to its own wage wj is a weighted average of the elasticities of each commuting ‡ow towards j, where the weights are given by the total contribution of residence r to location j 0 s labor supply. Labor supply to j is very elastic if large contributors to j have many alternatives, or have low commuting costs to other locations (i.e., if large contributors have small commuting ‡ows). Labor supply is very rigid if large contributors have just a few other alternative destinations, or those alternative destinations are very far. The labor supply to j is also a¤ected by wages prevailing in all locations connected to j. " (L (j) ; wj 0 ) is more negative when the local labor market of j has many locations, and when j 0 is very popular among large contributors to j 19 . Finally, if j 0 is not connected to j, wage changes in j 0 will 16
In a world where the size and the transportation infrastructure change across residence locations, di¤erences between r will re‡ect how easy it is for residents to respond to changes in wages for given commuting penalties drj . We will indeed …nd that, empirically, r grows with the measured area of r and decreases with the total length of roads present in it. 17 The set J 2 (j) is related to the two-neighborhood of j, and it would indeed coincide with it if, in the network of commuting paths, edges between locations would be undirected. Since I am in principle allowing j 2 J (r) but not r 2 J (j), the equivalence does not necessarily carry through, as it may not be possible to walk the network from j to j 0 . 18 Note that the use of the term "connected" is somewhat non-standard here, as j 0 may be connected to j even if there are no direct commuting ‡ows between them. 19 That is, if mrj 0 is high when Hr mrj =L (j) is also high.
14
not a¤ect labor supply in j directly. Note that, up to r , all the elasticities can be computed directly from data on commuting and location employment. Local labor markets for di¤erent j 2 R are generally overlapping: this is the …rst key element in the transmission of shocks through the territory. To understand the response of equilibrium wages in any j, the second piece of information to consider is the elasticity of labor demand. This is the aspect the next subsection addresses.
3.3
Production, consumption, and local labor demand
The production side of this economy follows closely a multi-sector version of Eaton and Kortum (2002), as in Caliendo and Parro (forthcoming), among others20 . There are S sectors (I denote with SM their set) which produce each a unit-length continuum of varieties tradeable both across locations at Home and with the foreign economy; in addition, there is a constant returns to scale, non-tradeable service sector s active in each location: residents in any r can only consume services produced locally (but of course, all those who work in r can contribute to its production, no matter where they live). I assume a common Cobb-Douglas sub-utility function for consumption across all locations in the world: a worker with income wj spends (s) wj on sector s, for s 2 SM [ fsg. Not all sectors are active in all locations. I denote with SM (j) the set of tradeable sectors active in j, and take it as given for all j. Following Eaton and Kortum (2002), the e¢ ciency z in production of oeach of nthese sectors’ o varieties is described by a n (s) (s) (s) , where Tj > 0 is the state of Tj z Frechet distribution, Pr Zj < z = exp technology in location j; sector s and > 0 is a dispersion parameter (for the RoW (s) economy, the state of technologies will be denoted by T ). If sector s is not active in (s) j, I set Tj = 0. Each variety is produced under constant returns to scale with labor only, and sold in a perfectly competitive market. I assume there are no intra-national transportation costs, and a common iceberg transportation cost (s) between any location j and the foreign economy: Hence, the share of expenditure on location j’s products in sector s, bought by any home location P (s) (s) (s) (s) (s) is j = Tj wj = (s) ; where (s) w , and w is the j2R Tj wj + T (s) (s) (s) (s) foreign wage; similarly, =T w = is the share of expenditure among 20
Other work adapting the Eaton Kortum (2002) framework to internal trade include Donaldson (forthcoming), Donaldson and Hornbeck (2013), Caliendo, Parro, Rossi-Hansberg and Sartre (2014).
15
residents in any home location on sector s goods coming from abroad21 . The foreign (s) (s) (s) (s) country spends a fraction j = Tj wj = of its sector s expenditure on P (s) (s) (s) (s) wj ; hence, it spends goods coming from j, where T w + j2R Tj P (s) (s) =1 a fraction j on its own goods. j2R P P To derive the local labor demand, let X = r2R Hr j2J (r) mrj wj be the the total national income in Home, and X = w H total national income abroad22 . Note that contrary to models where commuting is absent, X now depends on the equilibrium ‡ow of commuting choices across locations, among other things: when one wj changes, national income will change (also) because commuting ‡ows are (s) (s) reshu- ed. For a tradeable sector s, j (s) X + j (s) X is the total expenditure on labor in j to serve domestic and foreign demand. The non-tradeable sector produces (s) homogeneous services under constant returns to scale and a productivity Tj ; under perfect competition, (s) w~j Hj =wj units of labor are needed to serve local demand for P this good, where w~j = j 0 2J (j) mjj 0 wj 0 is the average nominal wage of residents in j.23 Hence, D (j) =
2
1 4 X wj
(s) j
(s)
X+
s2SM (j)
(s) j
(s)
X
+
(s)
3
w~j Hj 5
(9)
describes labor demand in j at wage wj . The second key element in the transmission of shocks across locations in the country (beyond the response of labor supply) is the response of labor demand to local wages around the economy. The elasticity of labor demand in j to changes in its wage is given by (see Appendix 21
(s)
(s)
The fractions j and do not depend on the destination location because we are assuming that 1) there are no intra-national transportation costs, and 2) (s) is the same irrespective of the destination in the domestic country. I make this choice as having origin-destination speci…c costs would require to estimate or to have available local prices of manufacturing goods. As we will see below, the model does deliver residence-speci…c price indices through the price of the local nontradeable service sector. 22 As we assume no trade de…cit, national income coincides with national expenditure. (s) (s) (s) (s) 23 Equality betwen demand and supply requires (s) w ~j Hj =pj = Tj Lj , where Lj is the labor (s)
(s)
(s)
~j Hj =wj = Lj : Note force employed in s. Since pj = wj =Tj because of perfect competition, (s) w that whenever wages of workers in j increase, the price of the non-traded service consumed by local residents in j also increases.
16
B.1 for details) " (D (j) ; wj ) =
X
1
(s) j
+
s2SM (j)
+ (s)
wj @ w~j w~j @wj
(s) j
(s)
wj @X X @wj
(s) j
(s) j
1
(s) j
+ (10)
1 (s)
(s)
(s) (s) where j X= (wj D (j)) and j j j X = (wj D (j)) are the share of labor payments going to employees in the s sector for domestic and foreign sales, (s) (s) and j w~j Hj = (D (j) wj ) is the share labor payments going to the non-traded sector. When wj grows, labor demand in j is a¤ected through several channels: …rst, the reduction in labor demand given everything else because of a higher wage; second, the loss of competitiveness at home and abroad, weighted by the share of labor necessary to serve that demand; third, the change in Home’s expenditure following the reshu- ing of commuting ‡ows; fourth, the change in the average income of residents, which a¤ects labor demand for local services, weighted by its labor share. Labor demand in j also responds to changes in wages elsewhere, creating linkages among locations on top of those generated by commuting ‡ows; in fact:
" (D (j) ; wj 0 ) =
8 P > > s2SM (j)\SM (j 0 ) > > > P > <
s2SM (j)\SM (j 0 )
> > > > > P > : s2S
M (j)
M j
P
h
(s) j
(s) (s) j0 j
+
(s) (s) j0 j
(s) (s) (s) (s) j0 j j0 j + wj 0 @ w ~j s + w~j @w 0 j j i (s) (s) (s) + 1+ j
(s) j .
wj 0 @X X @wj 0 w 0 @X + Xj @w j0
+
M j M j
j 0 6= j; ; j 0 62 J (j) j 0 6= j; , j 0 2 J (j) j0 = (11)
where s2SM (j) 0 If j is not a commuting destination (…rst row in (11)); j’s producers in all sectors where j and j 0 compete head-to-head have a relatively lower cost when wj 0 grows, thus raising labor demand. Moreover, a change in wj 0 has an impact on national income X (through reshu- ing of commuting ‡ows), thus changing labor demand in j for given competitiveness. If j 0 is a commuting destination (second row in (11)), the labor demand curve in j also moves since the average income received by residents in j changes, a¤ecting labor demand for local services. When the foreign’s wage grows ( j 0 = ; third row in (11)), D (j) unambiguously grows, since j becomes more competitive with respect to foreign producers both at home and abroad, and total
17
foreign expenditure X also increases for given competitiveness.
3.4
Equilibrium and prices
We are now in a position to write the system of equations that describe the general equilibrium. In an open economy with R residential and work locations, labor supply must equal labor demand everywhere: L (j) = D (j) 8j 2 R
(12)
R 1 of these equations are independent. In addition, total imports of all sectors must be equal to total exports at national level: X
s2SM
(s)
(s)
X=
X X
(s) j
(s)
X
(13)
j2R s2SM (j)
n o An equilibrium is a set of wages w = fwj gj2R ; w where (12) and (13) hold. In Appendix B.2 I prove the following propositions: Proposition 1 An equilibrium w exists. Proposition 2 Let w be an equilibrium; then this equilibrium is generically locally unique. The equilibrium might not be globally unique because the existence of commuting ties between locations may generate excess local labor supplies decreasing in their wages for some economies24 . Proposition 2 says, loosely speaking, that even if there were to be multiple equilibria, they would generically be locally unique25 , as it is always possible to slightly perturb the parameters of the economy to move away from pathological cases. 24
For this to occur, as a wj grows, the reshu- ing of commuting ‡ows must make X increase enough to overcome 1) the decrease in labor demand from j’s producers (to render D (j) increasing in wj ), and 2) the increase in L (j). This seems to be only a theoretical concern for the estimated model below, as 1) I perform checks starting from di¤erent initial conditions, 2) the correlation between simulated and actual wages across locations is 0.88 (see footnote 51 and Figure A3), and 3) the model o¤ers a way to check if the simulated economy is in such a case (see footnote 28 below), and this is never sati…ed at the equilibrium. 25 An equilibrium w is locally unique if there is a neighborhood of w in RR which does not contain another equilibrium.
18
Once wages are determined, commuting and goods’‡ows can be backed out from their respective equations. I normalize to 1 the price index for the manufacturing Q as = 1=(1 ) +1 (s) s = 1, where and > 1 is goods, i.e. s2SM s the elasticity of substitution between varieties within each sector. Hence, the price index in each location pr is just related to the price index of the local services, pr = s (s) s wr =Tr . The real wage of a resident in r commuting to j is simply wj =pr ; a and the average real wage of residents in r is w~r =pr . Having established properties of the equilibrium, we want to understand how an exogenous change in, say, the level of bilateral trade frictions, propagates throughout the economy and generates changes in local wages which are mutually consistent in general equilibrium. This is the question I address next.
4
The structure of transmission
A shock is an exogenous change in any parameter at the boundaries of this world economy. For example, the economy can experience changes in the level of bilateral trade frictions, or technology shocks in any of the Home’s sector-locations; roads can be built across the country reducing particular sets of origin-destination commuting costs; reforms can be implemented in the foreign economy that increase the productivity in some of its manufacturing sectors. The transmission of any shock has a common structure, that works through the speci…c responses of labor demand and supply analyzed in partial equilibrium above. Proposition 3 Let V be any exogenous parameter of the model. The elasticity of the
19
wage paid in any location j to a shock to V is " (wj ; V ) =
" (D (j) ; V ) " (L (j) ; V ) + " (L (j) ; wj ) " (D (j) ; wj ) | {z } direct e¤ ect
X
" (D (j) ; wj 0 ) " (L (j) ; wj 0 ) " (wj 0 ; V ) + " (L (j) ; wj ) " (D (j) ; wj ) 0 2 j 2J (j)nfjg | {z }
+
indirect e¤ ect from connected labor markets
X
" (D (j) ; wj 0 ) " (wj 0 ; V ) " (L (j) ; w ) " (D (j) ; w ) j j j 0 2RnJ 2 (j) | {z }
+
indirect e¤ ect from unconnected labor markets
" (D (j) ; w ) " (w ; V ) + " (L (j) ; wj ) " (D (j) ; wj ) | {z }
(14)
indirect e¤ ect from trade balance
for a wage in a domestic economy, and " (w ; V ) =
" (N X; V ) " (N X; w ) | {z } direct e¤ ect
X " (N X; wj ) j2R
|
" (N X; w ) {z
" (wj ; V )
indirect e¤ ect
(15)
}
in the foreign economy, where " (N X; ) is the elasticity of exports to a variable less the elasticity of imports to the same variable. Proof. See Appendix B.3. I describe the numerator of each of these three e¤ects in what follows. The denominator, common across terms, will be described below26 . The direct e¤ect The …rst term in (14) captures the net change in labor demand in j induced by a change in V directly, i.e., not mediated by changes in other locations’wages. Location j can be directly impacted from a change in V if and only if D (j) and/or L (j) are formally a function of V . Consider for example the impact of a change in the bilateral 26 Expressions for the elasticity of net exports to wages in a sector, of less analytic interest, can be found in Appendix B.3.
20
trade barriers in sector s, " D (j) ; (s)
(s)
(s)
(s)
; the direct e¤ect is
=
(
(s) (s) j
(s) (s) j
0 (s)
if s 2 SM (j) if s 2 6 SM (j)
(s)
(s) (s) where j X= (wj D (j)) and j j j X = (wj D (j)). If location j is active in s, this trade shock does impact j directly, because sector s is a source of labor demand for j (labor supply is never impacted directly). A decrease in (s) makes j’s producers less competitive at home but more competitive abroad, relative to foreign producers. In general, the net e¤ect on labor demand depends on the relative strength of these two changes, weighted by the share of the labor employed for production in each destination.27 If j; on the other hand, is not active in s, this shock has no direct impact in j (and j’s "exposure" to the shock would be zero). Nonetheless, L (j) and D (j) can still be impacted indirectly, via changes in other locations’equilibrium wages; this is what I analyze next. The indirect e¤ect from connected labor markets An increase in V has an equilibrium impact on wages in locations j 0 2 J 2 (j) n fjg, i.e. in locations connected to j. This change " (wj 0 ; V ), which we take as given in the second term of (14), will be in turn determined by an expression similar to (14) applied to j 0 . A change in wj 0 propagates to j through changes in labor demand (" (D (j) ; wj 0 )) and labor supply (" (L (j) ; wj 0 )), creating a (generally ambiguous) labor imbalance in j. Suppose for example wj 0 grows in equilibrium. Then, labor supply to j will decrease (through (8)), thus inducing an upward pressure on wj . Labor demand also changes, via changes in j 0 s producers’competitiveness, di¤erent demand for services, and change in national income (see eq. (11)); this imbalance must be closed with a change in wj . The indirect e¤ect from unconnected labor markets and trade balance As V increases, wages in locations j 0 not connected to j will also change in equilibrium. Changes in wages in these locations will not divert commuters away from j directly and in‡uence j only via labor demand (eq. (11)). The equilibrium change 27
Note the role of employment shares: in a unilateral liberalization only the share of labor employed to serve the domestic market (as opposed to all the sector’s employment) would be impacted; in a bilateral liberalization, the labor employed to serve the domestic vs. the foreign market enter with opposite sign. Data limitations typically hinder the ability to account for these distinctions in empirical exercises.
21
in w always increases labor demand in D (j) since j becomes more competitive and national income abroad grows, other things equal. The wage in the foreign economy The response of w to changes in V is summarized in eq. (15), which describes the adjustment in the foreign wage necessary to keep the trade balance (13) in equilibrium. The elasticity of w to V has again a direct e¤ect and an indirect e¤ect. As V changes, net exports of the home economy respond directly (for …xed wages): if they decrease on net as V increases, w must increase - making imports less competitive and exports easier - to restore trade balance; the magnitude of this change is regulated by the response of overall net exports to w at the denominator: a large, positive elasticity requires a smaller adjustment to w . As V changes, moreover, wages in all locations j change through (14) and net imports also change: this is the indirect e¤ect, and is a consequence of a non-trivial geography. In principle, net exports can increase or decrease through this channel: if they are on balance lower, then again w must increase to restore trade balance, and the adjustment is tempered by the sensitivity of net exports to w in the denominator. The denominator in all terms in (14) measures the sensitivity of the excess labor supply in j to changes in its own wage: the larger " (L (j) ; wj ) " (D (j) ; wj ), the smaller the adjustment in wages in j necessary to bring back the equilibrium in this local labor market.28 As argued above in eq. (11), the elasticity of labor demand encompasses the reduction in labor demand for given competitiveness, losses of competitiveness at home and abroad, and the increase in the income of residents. Note that in general, the direct e¤ect is the only one that characterizes the effects of di¤erent types of shocks; the propagation mechanism, however, only relies on equilibrium elasticities of any location’s demand and supply to other location’s wages. In a sense, when wj 0 is very elastic to a change in V , j 0 is more "central", i.e. its consequences have a larger impact on any other wj through the right-and side of (14) and (15); when " (wj 0 ; V ) ! 0, j 0 is acting as a shock-absorber: anything happening to wages in the economy is not propagating through j 0 . Indeed, these equilibrium elasticities are related to measures of centrality in network theory; Appendix B.4 28
Once the model parameters are estimated and the economy is simulated, one can check whether the sign of this denominator is positive (as it would be normal) or negative (which would occur in a pathological case where labor demand is strongly increasing in wj ); the latter case never occurs in the simulations. See also footnote 24.
22
makes the parallel more precise. Having completed the study of the transmission mechanism, I now describe the data used to estimate the model before discussing its identi…cation and estimation.
5
Data
In this section I turn to the description of data used, emphasizing some of their basic features. I start by describing data on commuting patterns, and then look at employment, wages, and sectoral distribution of the workforce. Data on expenditure shares across sectors, absorption, and trade frictions will be referred to when explaining the calibration of trade costs and expenditure shares in the next section.
5.1
Commuting
I construct commuting patterns using information in the U.S. Census of 2000, 5% sample and the American Community Survey (ACS) from 2005 to 2007 available from Ruggles et al. (2010).29 The universe comprises all employed people who do not live or work in Alaska, Hawaii, or Puerto Rico, or abroad, do not work in the Armed Forces, and have valid information on the place of work. A commuting pattern in the data is a reported place of residence and place of work. Since the model does not allow for individual level variation in hours supplied, I choose the empirical counterpart of mrj as the fraction of hours of employment from workers living in r which are supplied to j (and similarly, I identify employment in a location j with the total hours of work supplied in a year to j from residents anywhere). Geographic information on the place of residence and of work comes in PUMAs (Public Use Microdata areas). PUMAs are statistical geographical areas that contain a population of at least 100,000 persons in the 2000 Census, and provide the smallest geographical area available for public use in the Census and ACS. The continental United States is divided into 1,230 PUMAs. 30 29
Data to build commuting patterns is not available in the ACS before 2005. I stop in 2007 because ACS stops reporting data on weeks of work on a continuous basis (an information used when computing hourly wages) and only uses intervals, and to avoid contaminating the analysis with the impact of the …nancial crisis. 30 PUMAs of residence and of work use in most cases the same coding; occasionally, however, di¤erent PUMAs of residence are combined into a single larger PUMA of work: in these cases, I aggregate the PUMAs of residence as well to obtain a coherent sample of residence and job locations.
23
Table 4 shows the distribution of number of destinations reached by workers resident in each PUMA, by year (i.e., statistics on the out-degree distribution of the commuting network). The median PUMA has workers commuting to about 22 destinations, when using ACS data, and 47 destinations, when using Census.31 There is ample heterogeneity across PUMAs in the out-degree of each. Table 4: Number of Min p10 p25 2000 16 30 37 2005 5 13 17 2006 6 13 17 2007 5 14 18 ALL 5 14 19
destinations p50 p75 47 62 22 31 22 31 23 32 27 41
by PUMA, p90 Max 79 254 43 119 44 120 45 120 58 254
unweighted Mean N 52.56 1,230 25.81 1,230 26.12 1,230 26.86 1,230 32.84 4,920
This table reports selected percentiles in the out-degree distribution of commuting patterns, i.e. the number of PUMAs of work chosen by at least one worker from any PUMA of residence. The …rst row uses Census 2000, the following three ACS in the reported years, and the last aggregates all years. Each PUMA of residence receives weight 1.
A concern one may have is that the wide out-degree distribution is driven only by some small PUMAs. In Table A1, Appendix A, I replicate Table 4 weighting each observation with the total hours of work supplied by residents in each PUMA, and …nd that the distribution has actually a right-ward shift. I conclude that, despite being sizeable in terms of population, PUMA areas leave room for commuting patterns to emerge in the data. Even if the number of job locations typically reached is well above 1, it may still be that the fraction of hours supplied outside the PUMA of residence is small enough to make any analysis economically insigni…cant. To address this concern, I compute for each PUMA of residence the maximum fraction of hours across all its observed Due to Hurricane Kathrina, three PUMAs in Louisiana have been aggregated in 2006 as they would have not met the minimum population requirements otherwise. I aggregate them in the previous years as well for consistency. 31 The large di¤erence between Census and ACS statistics are due to the fact that Census samples many more individuals than ACS, and hence it is more likely to …nd individuals commuting to rare destinations. A number of robustness checks have been performed to make sure this is a reasonable explanation. While gas prices increased almost 4 times from 2000 to 2005, I found no changes in commuting times, commuting modes, or in commuting time by mode. The drop occurs across all States. I …nd that 99% of workers in 2000 commute to destinations which are also present in ACS: hence, it is only a small fraction of individuals which accounts for a halving in the number of destinations. These considerations all support the conjecture that the di¤erence is just due to sampling. In any case, estimates in the next section are performed using all the data, and then 2 subsamples (only year 2000, only 2005-2007, with and without time dummies) and there is no relevant change in our parameters of interest.
24
destinations, maxj mrj : ideally, we would like a distribution with a non-trivial left tail, i.e., that PUMAs of residence have most popular destinations which do not account for the almost totality of hours supplied32 . Table 5 shows that this is indeed the case: for half of the PUMAs, more than one-third of hours supplied commute outside. Table 5: Distribution of maxj mrj across all residences Min p10 p25 p50 p75 p90 Max Mean N 2000 0.16 0.34 0.49 0.67 0.82 0.91 0.98 0.64 1,230 2005 0.16 0.35 0.48 0.66 0.81 0.90 0.98 0.64 1,230 2006 0.18 0.35 0.48 0.66 0.80 0.90 0.99 0.64 1,230 2007 0.16 0.36 0.48 0.65 0.81 0.90 0.99 0.64 1,230 ALL 0.16 0.35 0.48 0.66 0.81 0.90 0.99 0.64 4,920 This table reports selected percentiles in the distribution of the fraction of hours commuting to the most popular destination. Speci…cally, for each PUMA of residence, the fraction of hours supplied to the most popular destination is computed; the table reports statistics on the distribution of such maximum. The …rst row uses Census 2000, the following three ACS in the reported years, and the last aggregates all years.
A crucial part of the transmission mechanism relies on the distance between two PUMAs. I approximate drj with the distance between their centroids33 , as the data does not provide individual distances traveled for work reason. Summary statistics on these distances across all workers are presented in Table 6. The unrealistically high maximum commuting distances are due to the fact that, for some occupations, the job location is itinerant34 . In the estimations of relative commuting ‡ows, I will repeat all estimates twice, for the complete sample and a truncated one which eliminates the top 1% of commuters by distance: in the restricted sample, results are actually strengthened, in the sense that the implied elasticities of relative commuting ‡ows to relative wages are higher35 . 32
In a strong majority of cases, the most popular PUMA of work is the PUMA of residence. In 8% of the PUMA of residence-year observations (396 out of 4920) this does not happen: these PUMAyears are on average 3.4 smaller in terms of size, have a 1.5 denser transportation network (total length of major and minor highways, major roads, and railroads divided by PUMA area) and are around twice as dense in terms of hours of labor supplied by residents, or resident population at or above 16 y/o, per square mile of PUMA. 33 I compute the distance using the Haversine formula. Centroids of each PUMA have been computed using standard spatial analysis software and requiring that the centroid falls within the PUMA itself. 34 The questionnaire asks the job location in the week preceding the interview. I …nd, for example, that aircraft pilots and engineers, transportation attendances, actors, entertainers and performers, marine engineers and naval architects, are between 10 and 40 times overrepresented in the sample of commuters with distance higher than 1,000 miles, with respect to their proportion in total employment. 35 The top 1% of commuters report distances beyond 136.4 miles. While any selection would
25
2000 2005 2006 2007 ALL
Table 6: Distribution of commuting distances p50 p75 p90 p99 Max Mean N 0 14.68 34.45 131.93 2764.38 14.68 234.5 0 15.67 36.31 150.46 2742.95 15.93 250.1 0 15.41 36.07 151.59 2754.01 15.80 260.0 0 15.68 36.36 160.86 2713.49 16.03 262.4 0 15.41 36.04 147.91 2764.38 15.63 1,007.1
This table reports selected percentiles in the distribution of commuting distances, in miles. The length of a commuting pattern is computed as the distance between the centroids of the reported PUMAs of residence and of work, using the Haversine formula. Centroids of each PUMA have been computed using standard spatial analysis software and requiring that the centroid falls within the PUMA itself. The …rst row uses Census 2000, the following three ACS in the reported years, and the last aggregates all years. Each observation receives a weight proportional to the yearly hours of labor supplied. The last column reports total hours worked in a year, in billions.
As one can expect, commuting ‡ows decrease with distance, and this relation is consistent across Census and ACS sample. Figure A1 in the Appendix plots the fraction of hours ‡owing from any given r to one observed destination j, mrj , in a year against the distance between the centroids of the two PUMAs. This negative relation fades away after a certain distance (interestingly, around the top 1% cuto¤), consistent with the fact that long distances are due to itinerant occupations and do not really re‡ect daily commuting patterns. Commuting ‡ows decrease with distance with an elasticity of 1:13 in the complete sample, and 2:54 in the truncated sample, after controlling for year, origin and destination …xed e¤ects36 .
5.2
Employment, hourly income, and geographic distribution of industries
The total residential population of a PUMA Hr is the sum across all employed persons living in r of their usual hours of work per week times the number of weeks worked in the preceding year. Total employment in a PUMA is the sum across all the workers working in PUMA j of the same quantity37 . Table A2 reports summary statistics on be arbitrary, I consider this choice reasonable: the computed distance is between centroids, but the worker may just live on one side of the border between two PUMAs and work on the other; moreover, as Figure A1 will show, the negative relation between bilateral distance between PUMAs and fraction of commuters changes around this distance. 36 Origin and destination …xed e¤ects contribute substantially to the measured elasticity of commuting ‡ows to distance. Analogous regressions run only with year …xed e¤ects have a slope of 0:96 and 1:55, respectively. 37 Person weights are used throughout the analysis and we will avoid repeating it in the description.
26
hours supplied to a given PUMA of work over time. To compute the average income of hours supplied to a location, I sum the total income received by all employed people in j (pre-tax wage and salary income, plus pre-tax self-employment income from a business, professional practice, or farm, if present), and divide by the total hours worked there: this value will be used as the empirical counterpart of wj .38 All monetary values are in 2007 dollars. Table A3 reports some summary statistics on these hourly income across PUMAs of work. I close the description of basic patterns in the data summarizing some relevant aspects of the geographic distribution of sectoral activity. To this purpose, I convert the industry of employment of each worker from the Census/ACS codi…cation into 3-digit NAICS in the 2002 classi…cation using the crosswalk made available by Ruggles et al. (2010). The …rst three digits are identical to the NAICS1997, in which international trade data is also provided. I limit the sector-level analysis to 21 manufacturing sectors (NAICS 311-339) and pool all the others sectors into a residual service, non-tradeable sector. PUMAs vary substantially in terms of how many sectors are active, and in their manufacturing employment share (Table A4). Sectors also vary in terms of employment concentration: moving from sector at the 25th to the 75th percentile, the top 5% of PUMAs account between 32% and 57% of total sectoral employment (Table A5).39 This variability in the sectoral composition and manufacturing employment share across PUMAs, along with di¤erences in the concentration of sectoral employment, create wide scope for the propagation of shocks and give latitude to estimate technology parameters.
6
Identi…cation and estimation
In this section I show how di¤erent variation margins can be used to identify the parameters of labor job location choice across PUMAs of residence and technology parameters across PUMAs of work. 38
We have considered using only salaried employees. This would come at a price of excluding part of employment from our analysis, while the model does not distinguishes between di¤erent forms of income. Since the correlation between hourly income and hourly wage at PUMA of work level is 0.9951, it seems reasonable to proceed with a more complete picture of total hours of work supplied. 39 Summary statistics on each sector can be found in Table A6.
27
6.1
The choice of job location
One key piece of information to perform counterfactuals is the set of parameters r , which regulate the elasticity of commuting ‡ows to changes in relative wages. From (5), one can compute 1 wj 1 drj mrj = log log log mrr wr drr r r for any pair of origin-destinations observed in the data. The intuition is the following: when r is very small, people are very similar and even small di¤erences in relative wages are re‡ected in large di¤erences in relative commuting ‡ows; when r is very large, on the other hand, idiosyncratic preferences are the main factor determining job destination, and even large di¤erences in relative wages do not impact relative commuting ‡ows signi…cantly. The fact that di¤erent PUMAs have di¤erent geographical size and di¤erent levels of infrastructure development requires an estimation of r speci…c for each residence location: hence, I will model r = 0 Roadsr 1 Arear 2 ; a (reduced form) function of the the total length of major highways, minor highways, major roads and railroads present in each of the PUMA, and the total area of each PUMA, which I have computed directly using digital maps from ESRI. I decompose drj = OppCostrj1 (Roadsr Roadsj ) 2 (Arear Areaj ) 3 ~"rj , a function of the product of total roads’length in r and j, the product of the total areas of r and j, the average opportunity cost of commuting time of workers from r to j, and a disturbance term. To compute the opportunity cost of time, I multiply the hourly income of each commuter from r to j times twice the commuting time that this worker reports in the data, and compute a weighted average of this cost across all commuters. After substituting these expressions40 , log
mrj = mrj 1 0
+
1 0
Roadsr 1 Arear
Roadsr 1 Arear
2
2
2
log
Roadsj Roadsr
log
wj wr
1 0 1
0
OppCostrj OppCostrr Areaj + "rj(16) 3 log Arear
Roadsr 1 Arear
Roadsr 1 Arear
2
2
1
log
Of course, according to the model equilibrium wages do depend on commuting costs drj and drr (and hence on ~"rj =~"rr ) so that a simple non-linear regression would 40
h
Here, ~ "
rj log ~"rr
~ "
= i
1 0
Roadsr
1
Arear
2
~ "
rj E log ~"rr
rj E log ~"rr .
28
and
"rj
=
1 0
Roadsr
1
Arear
2
w
su¤er from the correlation of log wrj with the unobservable. The model however suggests that (functions of) the relative measure of agents living in a location j vs. location r, (Hr and Hj ) or living around location r but not in r are valid instruments as they a¤ect relative commuting ‡ows only through relative wage, and are uncorrelated with "rj (which is only function of parameters and i.i.d errors). I will use as instruments the log of four ratios: total labor force (not just employment) living in j divided by r; total labor force living in PUMAs whose centroid is less than 200 miles away from j (but not in j) divided by the same quantity for r; and the same two ratios, computed using total population 16 years old and older rather than total labor force. These instruments are valid within the model as Hr are parameters and are not contained in "rj ; they are valid empirically as long as the ratio of (say) population living in two neighboring areas is not correlated to i.i.d. shocks to unobserved components of commuting costs (e.g., unexpected road closures). I estimate this model with GMM, clustering errors at the level of PUMA of residence, only for data in the year 2000 (i.e., with Census data), for the years 2005-2007 (i.e., with ACS data), and for the whole sample; I repeat these estimations using all recorded commuting patterns …rst, and then truncating away recorded origindestinations whose PUMA centroids are more than 136.4 miles apart (i.e., the top 1% of commuters by distance). The main results are presented in Table 7.41 The main coe¢ cients of interests 1 and 2 are very precisely estimated and are stable across subsamples. As expected, a denser transportation network facilitates the response of commuting ‡ows to di¤erences in wages ( 1 < 0, so that more roads increase 1= r and make commuting ‡ows more elastic), while a larger PUMA area makes the measured elasticity smaller ( 2 > 0, so that in a larger PUMA 1= r is smaller and commuting ‡ows are less responsive to di¤erences in wages). Moving from the complete to the truncated sample increases the sensitivity of r to roads and PUMA areas42 . Table 8 below shows summary statistics for the distributions of 1,230 43 r parameters estimated using all years for the unrestricted and restricted samples . 41 The full set of coe¢ cients is reported in the Appendix, Table A7. I also repeat the same estimation introducing year dummies for the constant, which allows for di¤erent average ~"rj =~"rr over time, with essentially unchanged results. These estimates are reported in the Appendix, Table A8. 42 Both coe¢ cients increase in absolute values. I will use the estimates of r and all other parameters from the restricted sample in the counterfactual exercises, as they correspond to a clean version of the data with realistic commuting possibilities. 43 All the estimated r in the unrestricted sample are signi…cantly di¤erent from zero at less than
29
Table 7: GMM estimation of parameters of job location choice All distances Truncated distances Only 2000 Only 2005-07 All years Only 2000 Only 2005-07 All years 0
1
2
N
3.44***
4.46***
4.43***
5.38
4.99
4.03
(0.89)
(1.29)
(1.03)
(4.42)
(3.98)
(2.96)
-0.44***
-0.41***
-0.43***
-0.78***
-0.73**
-0.68**
(0.08)
(0.07)
(0.07)
(0.26)
(0.30)
(0.27)
0.23***
0.22***
0.22***
0.43***
0.41***
0.39***
(0.05)
(0.04)
(0.04)
(0.13)
(0.15)
(0.14)
64,654
96,912
161,566
32,397
65,078
97,475
This table shows selected coe¢ cients in the GMM estimates of eq. 16. Each column reports the results of a particular GMM estimate: columns di¤er only according to the sample used. The …rst three columns use all observed bilateral commuting ‡ows; the last three only bilateral commuting ‡ows between PUMAs whose centroids are less than 136.4 miles away from each other (i.e., exclude the top 1% of commuters). Within each set of three columns, the …rst uses only commuting data from then Census 2000, the second only data from ACS 2005-2007, and the third all data together. * p < 0.1; ** p < 0.05; *** p < 0.01. Standard errors in parentheses.
Table 8: Distribution of estimates of r Min p10 p25 p50 p75 p90 Max Mean N Unrestricted 0.44 0.70 0.76 0.82 0.88 0.95 1.36 0.82 1,230 Restricted 0.14 0.27 0.32 0.36 0.41 0.47 0.87 0.37 1,230 This table reports selected percentiles in the distribution of the estimates of the parameter r implied by the estimation of eq. 16 reported in Table 7. The …rst line refers to estimates based using the whole sample of commuting patterns (third column), and the second line to estimates based on the restricted sample (sixth column).
These estimates of r can be plugged in eq. (8) to estimate " (L (j) ; wj 0 ) for any pair of j,j 0 . Figure 1 shows for example the elasticity of labor supply to two particular PUMAs, Boston (MA) and Manhattan, in New York (NY) to wages in the same area (positive, in green) and to neighboring areas, for 200544 . Interestingly, wages in Manhattan may a¤ect what happens in Boston (by diverting away workers who can commute to both destinations). It is clear that one can draw a similar picture for all the PUMAs between these two urban areas: local labor markets continuously overlap over the territory45 . 1% signi…cance; about 94% of the r in the restricted sample are signi…cantly di¤erent from zero at 5% signi…cance. PUMAs with r not signi…cantly di¤erent from zero are on average 2.9 times smaller than the average PUMA, and have a 2.4 times denser road network (measured in miles of roads per square mile of PUMA area). For these PUMAs, relative commuting ‡ows are extremely sensitive to relative wages. 44 I use the estimates from the restricted sample. The correlation of these elasticities across di¤erent years is always above 0.99, so these pictures are well representative. 45 As another example, Figure A2 shows the elasticity of labor supply to a location j with respect
30
Figure 1: Elasticity of labor supply to a PUMA to wages around it
Cambridge
Worcester Boston Springfield
Providence
Hartford Waterbury Manchester
New Haven Bridgeport
Lowell Cambridge
Stamford
Boston
Paterson
Worcester Springfield
Newark
Elizabeth Providence
Allentown
Yonkers
New York
Edison
Hartford Waterbury New Haven Bridgeport Stamford Yonkers
New York
Philadelphia
2.24
2.62
-0.001 - 0.00
-0.001 - 0.00
-0.07 - -0.04
-0.15 - -0.05
-0.24 - -0.16
-0.60 - -0.57
-0.03 - 0.001
-0.04 - -0.001
-0.15 - -0.08
-0.56 - -0.16
This …gure shows the elasticities "(L(j); wj 0 ) for PUMAs 2503300 (Boston, MA) and 3603800 (Manhattan, NY). Elasticities are computed using observed data on commuting ‡ows in 2005 and estimates of r from the restricted sample reported in table 8.
Once we have obtained the estimates from eq. 16, we can recover all the drj (with the normalization drr = 1). To run counterfactual simulations, we still need to …nd parameters on the technology side of the model, which is the subject of the following subsection.
6.2
Technology parameters
The technology is described by the dispersion parameter and the location parameters (s) Tj . Since identi…cation will come from time variation, I introduce time indices in the subsequent expressions; also, to reduce the dimensionality of the problem, (s) (s) I assume that Tjt = Tj T (s) e"jt , i.e., the productivity of a location in a sector is coming from characteristics speci…c to a location but common across sectors, Tj , and characteristics speci…c to a sector but common across locations, T (s) , plus an to the prevailing wage in the same area, " (L (j) ; wj ) for the whole U.S. and zooming on the New York-Boston area.
31
n o (s) idiosyncratic component log-normally distributed, exp "jt . Consider the wage bill (s)
of sector s in j, Wjt = (s) jt , (s)
log Wjt = log
(s)
(s) jt
(s)
Xt +
T (s) + log Tj
(s) j
(s)
X t ; using the expressions for
log wjt + log
"
Xt (s) t
+
(s)
X
t (s) t
#
(s) jt
and
(s)
+ "jt
which says that in principle, can be estimated with a regression of the log wage bill paid to a sector-location-year on sectors, locations, and sectors-year …xed-e¤ects and the hourly compensation received by workers in a given location. The intuition is the following: comparing all locations that have the same sector s active, if the strength of comparative advantage is low (i.e., is high and goods are homogeneous in terms of productivity) a slightly higher prevailing wage in j would make sector s less competitive in a wide range of varieties everywhere, and reduce heavily total labor demand (and hence total wage bill) for workers in this sector. On the contrary, if productivities tend to be dispersed, it takes a relatively larger increase in wj to reduce the range of varieties for which j is the lowest cost producer by the same amount. Note that a similar regression could be run with the total number of hours worked (s) in sector s location j, Hj;t , on the left-hand side, and the coe¢ cient on wages would then be ( + 1) rather than : while the model forces the wage to be identical across sectors in a location, this will not be true in general in the data, and hence the two approaches are not necessarily equivalent. I will explore both alternatives. One concern with this regression is of course endogeneity: the idiosyncratic shocks (s) (s) "jt is part of the productivity Tjt , is not observed, and wages wjt do depend in (s) equilibrium on it. It could be that a higher "jt increases both the wage in a location and the total labor demand in sector s, thus biasing the estimate of the coe¢ cient upwards, towards positive values. To address this issue, I note that the resident population and labor force in location j or around it are valid instruments according to the model. These instruments are also empirically valid as long as the distribution of population across locations is not correlated to i.i.d. shocks to productivity (e.g. unforecastable equipment breakdown for …rms in a sector-location). I will exploit variation in the labor force and resident population over time within location-sector
32
cells to identify . I run a 2-stages least square of the form (s)
= log
(s)
T (s) + log Tj +
(s) t
(s)
= log
(s)
T (s) + log Tj +
(s) t
log Wjt
log Hjt
(s)
(17)
log wj;t + "j;t
(s)
( + 1) log wj;t + "j;t
(18)
(s)
where log (s) T (s) is a sector dummy, log Tj is a location dummy, t is a year-sector dummy, and instrumenting wj;t with (combinations of) the log of labor force and resident population in j and around it. The results of these estimations are reported in Table 9.46 Table 9: Coe¢ cient
in estimation of eq. 17 and eq. 18 Dep. var: wage bill Dep. var: tot. hours N +1 N
OLS
-0.61***
78,292
(0.12)
IV: only local
7.69***
78,292
(1.77)
IV: local and 50 miles
78,292
8.60***
78,292
(1.59)
4.93***
70,271
(1.37)
IV: local and 200 miles
-0.08 (0.10)
5.37***
70,271
(1.22)
3.74** (1.47)
78,292
4.16***
78,292
(1.29)
This table shows estimates of equation 17 (left column, reporting ) and equation 18 (right column, reporting + 1). The …rst row shows results for an OLS regression of the dependent variable (total wage bill or total hours in location j and sector s) on sector, locations, and sector-year …xed e¤ects. The second row show IV estimates of the same equations, where the instrument is the total population 16 y/o and older and labor force living in j. The third and fourth rows add population 16 y/o and older and labor force in PUMAs whose centroid is within 50 miles, or within 200 miles, from the centroid of j, respectively. * p < 0.1; ** p < 0.05; *** p < 0.01. Standard errors in parentheses.
The two columns report results when the dependent variables are total wage bill and total hours worked, respectively. The …rst line reports the value of with simple OLS estimates of these equations. As can be seen, the coe¢ cient is positive (implying a negative value for ): unobserved productivity in a sector/location generates a positive correlation between hourly wage and total wage bill. Once we use the log of total population and labor force (second row) as an instrument, however, the coe¢ cient is negative and precisely estimated. The second and third rows add log population and labor force within 50 miles, and within 200 miles of the PUMA, respectively. As we 46
Again, repeating the estimation with year dummies leaves results essentially unchanged. These estimates are reported in the Appendix, Table A9.
33
would expect, adding instruments which are arguably less able to shift labor supply makes the endogeneity problem somewhat more apparent, and decreases the estimates of . Note also that the coe¢ cients on hours are typically below (but not exactly 1 less than) the coe¢ cient on wages, con…rming the importance of within-location, betweensectors variability in wages47 . In what follows, we will use the benchmark value of = 7:69: With these estimates, we are in a position to recover the technology location (s) parameters. The values Tj , (s) T (s) ; are estimated directly from (17), and "j is a residual for each sector-location-year. To calibrate the shares (s) in the utility function, I set the share of non-manufacturing expenditure to M = 0:78 (Dekle Eaton and Kortum, 2008). I further merge the NBER Productivity Database and NBER International Trade U.S. Imports and Exports from 2000 to 2006 and aggregate the values at the 3-digit NAICS to obtain the share of expenditure by sector (s) as 0:22 times the share of U.S. absorption of s on total manufacturing absorption48 . Hence, we can obtain values for T (s) . (s) Note now that we can read the import penetration from the data49 . Using (s) (s) (s) (s) and solving for T , the model suggests Tj = Tj T (s) e"j in the expression for (s)
T
(s)
=
P
(s)
j2R
1
(s)
(
Tj e"j wj
(s) w
)
T (s)
Up to the wage in the foreign country, everything on the right-hand side is known. To …nd a value for the average hourly income in the rest of the world, I resort to the Penn World Tables, version 8. We want to compute a wage for the foreign economy that is consistent with the data on employment in the United States in the Census/ACS. In the years 2000-2007, the United States represent about 5% of the world employment (and also of the world population): hence, H = 0:05 (H + H ), where H is the total hours worked on average by the U.S. employment. I then set H = H 0:95=0:05 = 4; 784 billion hours. Similarly, the United States represent about 22% of world GDP, 47
The number of observations when instrumenting with population and labor force within 50 miles drops as some PUMAs have no other centroids within 50 miles of theirs, resulting in a missing value (log (0)) for the instrument. P 48 0 That is, I set (s) = 0:22 (V (s) N X(s)) = N X(s0 ) where here V (s) is s0 2SM V (s ) total value of production in s and N X (s) are its net exports. (s) 49 In particular, = I (s) = (V (s) N X (s)), where here I (s) denote imports of sector s, V (s) is the total value of production and N X (s) are net exports.
34
i.e., X = 0:22 (X + X ); hence, w = X =H = (X=0:22 X) = (H=0:05 H) = (wH=0:22 wH) = (H=0:05 H) = 4:14, where w is the average hourly income in (s) the United States. With w in hand, we can back out T . I set the productivity of the non-traded sectors at home and abroad at the mean value of the productivities of their manufacturing sectors. Finally, I use the cost of freight, insurance, and tari¤s paid at the border for U.S. imports from the same International Trade dataset to impute values for the trade costs (s) at each of these sectors.50
7
The real wage incidence of trade integration
With the parameters of the model in hand, I simulate the equilibrium value of wages in 2005. Figure A3 shows that across PUMAs, simulated wages and wages in the data exhibit a very high correlation.51 In the following subsections, I …rst explore the consequences of eliminating trade frictions in a single sector across exposed and unexposed locations; I then assess the ability of exposure to trade to predict real wage changes.
7.1
Liberalization in a single sector
In this simulation, I study the impact of a complete elimination of bilateral trade frictions in NAICS sector 334, "Computer and Electronics Product Manufacturing" (CEP) across PUMAs. I will refer to this change as a "trade liberalization" for brevity52 . To study the impact of a liberalization I simulate the model twice: …rst 50
(s)
Summary statistics on (s) , and (s) are again presented in Appendix, Table A6. This fact is reassuring in light of the possible multiplicity of equilibria, as it signals that the equilibrium to which the simulation converges is similar to the equilibrium being observed in the data. See also footnote 24. 52 This sector is chosen for a variety of reasons. CEP is, among 3-digit NAICS, the one with lowest bilateral trade frictions (tari¤ plus freight and insurance), = 1:0204 on average between 2000 and 2006 (as computed with the CIF/FOB ratio from the NBER-International Trade Database): hence, it gives a lower bound on the e¤ect of a one-sector liberalization. It is also one where the revealed comparative advantage of U.S. vs. the rest of the world is among the highest (Costinot, Donaldson, Komunjer 2012). CEP accounts for 9.5% of manufacturing employment and 1.2% of total employment, in terms of hours, and it is relatively highly concentrated: the top 5% of PUMAs account for 57% of total employment in the sector, placing it around the 75th percentile across sectors (see again Table A5, panel B); the remaining 95% of PUMAs do not contribute more than 0.3% of hours each; 250 PUMAs report exactly zero employment in this sector. This makes the sector ideal to study the propagation in inactive and active locations. 51
35
with the parameters estimated and calibrated as described above, and then setting (334) = 1 rather than 1:0204. Each simulation computes the equilibrium wages paid to workers employed in each location and hence all other outcomes. I then compare outcomes before and after the elimination of the trade frictions. Table 10 shows that in the median PUMA, this liberalization implies an increase of the average wage paid to workers of 0.224%, and a movement from the minimum to the maximum impact covers about 39% of this median. Importantly, if we condition on whether the PUMAs have positive employment in the sector or not, we …nd that the order of magnitude of the impact is comparable between the two categories. In other words, even if the distribution of impact on PUMAs not active in CEP is slightly shifted to the left, being inactive in the sector is not enough to be shielded from the consequences of this (admittedly small) liberalization, and the impact is typically almost as big as the one measured in locations active in CEP. Table 10: Log changes (x100) in Min p10 p25 p50 All 0.190 0.203 0.219 0.223 Positive 0.215 0.219 0.222 0.225 Zero 0.190 0.194 0.198 0.204
wages of workers across PUMAs p75 p90 Max Mean N 0.227 0.231 0.277 0.221 1,230 0.228 0.232 0.277 0.226 980 0.211 0.217 0.225 0.205 250
This table shows the distribution of the impact of an elimination of trade frictions in NAICS 334, "Computer and Electronics Product Manufacturing" on nominal wages of workers across PUMAs. The …rst row reports the distribution of impacts across all PUMAs, the second across PUMAs active in sector 334, the third across PUMAs inactive in sector 334.
Where do these e¤ects come from, and in particular, why are locations not active in CEP impacted nonetheless? Following Proposition 3, we can decompose the change in wage exactly in its four components53 . Table 11 shows the average importance of each term, for all PUMAs, and distinguishing them by whether or not the PUMA is active in the sector (Figure A4 in the Appendix shows the distribution of each of these components across PUMAs). For the average PUMA j with no employment in CEP, a little more than 61% of the e¤ect occurs because connected locations (whether they are active in CEP or not) experience an equilibrium change in wage, and this change has an impact on local labor supply and local labor demand; one-eight of the 53 While Proposition 3 applies to in…nitesimal changes, R 1:0204 wj ( (334) ) " wj (334) ; (334) d and then use (334) 1 334 (334) " wj ; in separate terms. I split the interval ulate the model for points on the grid, and approximate terms.
36
we can always write:
dwj
=
the Proposition to decompose 2 [1; 1:0204] in 10 intervals, simthe integral with a sum of …nite
total e¤ect happens because locations which are far enough from j to a¤ect its local labor supply, a¤ect nonetheless its local labor demand via overlaps in the set of active sectors; the remaining one-fourth is attributable to international trade rebalancing. Among locations with positive employment, only 8% of the total e¤ect is attributable to the direct e¤ect of removal of bilateral frictions on labor demand in a location.54 Table 11: Decomposition of the e¤ects of a liberalization in CEP Zero Empl. in CEP Positive Empl. in CEP Overall Direct E¤ect 0.0 8.1 6.4 Connected L.M. 61.4 60.3 60.5 Unconnected L.M. 12.2 8.4 9.2 Trade Balance 26.4 23.3 23.9 Total 100 100 100 This table shows the contribution of each of the terms in Proposition 3 to the change in wages across PUMAs following a reduction of trade barriers in CEP from 1.0204 to 1. The …rst column reports the average for PUMAs with zero employment in CEP, the sectond column for those with positive employment in CEP, and the third for all PUMAs.
These considerations are important for empirical studies who build measures of exposure to trade based on local employment characteristics: in general, because a positive exposure to some sectors does not control for equilibrium in‡uences arising from other sectors and locations; and in particular, because these measures constrain the empirical exercise to silence on the impact of trade on unexposed locations. Since the model generates changes in real wages which are typically hard to observe in the data, we can ask how exposure to this policy experiment impacts real wages across the United States. I compute exposure in location r as (334) = r (334) P (s0 ) 0:0204 Hr = s0 2SM (r) Hr , the cut in trade frictions times the share of manufacturing (Kovak, 2013) employment in sector 334 present in job location r. I regress wages of workers in r, nominal wages of residents in r, and real wages of residents in r on this exposure. The associated coe¢ cients (334) are summarized in Table 12, r where panels di¤er according to the weight put on each observation. As the United States have a comparative advantage in CEP, a larger exposure implies a larger increase in nominal wages, d ln wr (…rst column of each panel). As equilibrium wages around r change for given commuting patterns, and the job location composition of 54
Note that the direct e¤ect in active locations is not simply spreaded equally among the other channels in the inactive locations. In fact, only the relative importance of trade rebalancing is on average the same for active (23:3=0:919 = 25: 4) and inactive (26:4) locations. The contribution of connected labor markets is relatively more important in active locations (60:3=0:919 = 65: 6 vs. 61:4), presumably because connected labor markets also tend to be active in CEP.
37
j’s residents endogenously responds, the average nominal wage of residents in j also increases, although the association is slightly ‡atter and less systematic: the R2 falls of about 20 percentage points. The change in exposure is however not able to predict the change in real wages (third column): both the slope and the R2 of the regression go to zero55 . The reason for this result is that when wages of workers in a labor market increase, the price of local services also increase, and since non-traded services have a large expenditure share, the real wages changes have a very weak association with nominal wages changes. These results emphasize that unavailability of local prices may be consequential in the evaluation of the impact of trade integration on local labor markets. Table 13 shows the actual changes in real wages of residents across PUMAs. Two messages emerge: 1) there is basically no di¤erence in the distribution of gains of exposed and unexposed locations, and 2) changes in the price of local services erode around 75%-80% of the gains in nominal wages. Table 12: Exposure to liberalization in CEP and local wages B: Weighted by empl. in 334
A: Unweighted d ln wr (334) r
const R2 N
d ln w ~r
d ln(w ~r =pr )
0.130***
0.095***
-0.007***
(0.011)
(0.009)
(0.002)
0.002***
0.002***
0.000***
(0.000)
(0.000)
(0.000)
0.52 980
0.33 980
(334) r
const R2
0.02 980
N
C: Weighted by empl. in mfg d ln wr (334) r
const R2 N
d ln w ~r 0.163***
0.004
(0.006)
(0.007)
(0.003)
0.002***
0.002***
0.000***
(0.000)
(0.000)
(0.000)
0.77 980
0.58 980
0.00 980
d ln w ~r
d ln(w ~r =pr )
0.186***
0.144***
-0.001
(0.009)
(0.009)
(0.003)
0.002***
0.002***
0.000***
(0.000)
(0.000)
(0.000)
0.76 980
0.56 980
0.00 980
D: Weighted by total empl.
d ln(w ~r =pr )
0.203***
d ln wr
(334) r
const R2 N
d ln wr
d ln w ~r
d ln(w ~r =pr )
0.156***
0.121***
-0.001
(0.009)
(0.008)
(0.002)
0.002***
0.002***
0.000***
(0.000)
(0.000)
(0.000)
0.64 980
0.47 980
0.00 980
(334) This table shows 4 panels of OLS estimates of equations of the form d ln yr = const + (334) , r r (334) where each panel weighs observations as indicated. r is the exposure of location r to liberalization in CEP as de…ned in the main text. In each panel, the …rst column shows results for yr = wr , the nominal wage of workers in r, the second for yr = w ~r , the average nominal wage of residents in r, and the third for yr = w ~r =pr , the average real wage of residents in r. *** p < 0.01. Robust standard errors in parentheses.
As a …nal note, it is interesting to compare these predictions with those of a model where each labor market is isolated, as empirical studies tend to assume absence 55
The slope becomes slightly negative, if we weigh large and small locations equally.
38
Table 13: Log changes (x100) in Min p10 p25 All 0.041 0.047 0.048 Positive 0.041 0.047 0.048 Zero 0.042 0.045 0.047
real wages of p50 p75 0.049 0.050 0.049 0.050 0.049 0.050
residents wage across PUMAs p90 Max Mean N 0.051 0.057 0.049 1,230 0.051 0.056 0.049 980 0.052 0.057 0.049 250
This table shows the distribution of the impact of an elimination of trade frictions in NAICS 334, "Computer and Electronics Product Manufacturing" on average real wages of residents, across PUMAs. The …rst row reports the distribution of impacts across all PUMAs, the second across PUMAs active in sector 334, the third across PUMAs inactive in sector 334.
of linkages between labor supply in di¤erent locations. To perform this exercise, I manipulate the matrix of commuting possibilities so that residents in any r can only work in r itself, and repeat the analysis above: I compute the change in wages dwjN C following a reduction in (334) from 1.0204 to 1. The quantity ln dwjN C =dwj measures the percentage overprediction (or underprediction, if negative) in wage changes that one would incur into when considering each labor market in isolation, while the true data-generating process includes commuting possibilities. Figure A5 shows that a model with no commuting would over-predict wage changes in locations active in CEP, while under-predicting changes in regions inactive in it. This is indeed intuitive. In the data generated by the true model, large increases in labor demand in a location can be partially accommodated by labor ‡owing in from neighboring places. If we shut down this possibility, the equilibrium increase in wage in locations expanding relatively more (less) must be stronger (weaker) to bring the equilibrium back in each local labor market.56 Note that the extent of overprediction will typically depend by how large are the geographical units of observations, although in general we have seen that absence of commuting ties does not necessarily imply absence of linkages among local labor supplies.
7.2
Gains from trade
In this subsection, I investigate the gains in real wages of residents across the United States implied by a movement from autarky to the current level of trade frictions: I simulate the model with the vector of trade costs approaching in…nity and comparing 56 One may wonder whether there is at least a positive relation between dwjN C and dwj : if that were the case, we could at least hope that the bias in the prediction of the impact of trade is constant across locations. Figure A6 in the Appendix shows that while there is a positive relation between dwjN C and dwj in locations where CEP is active, the realized change in wage dwj has basically no relation with dwjN C in locations where CEP is inactive.
39
Figure 2: Gains from trade
2.76 - 3.22 3.23 - 3.32 3.33 - 3.41 3.42 - 3.55 3.56 - 3.90
This …gure shows a map of percentage increase in real wages of residents across U.S. PUMAs following a movement from autarky to the current level of trade frictions. Lighter lines are PUMAs boundaries, and bolder ones indicate state boundaries.
the resulting outcomes with the baseline simulation. I …nd that the average real hourly wage in the United States is about 3.3% higher because of trade. This value is larger than typical estimates of trade models with one frictionless labor market (for example, Eaton and Kortum (2002) estimate gains of 0.8%-0.9%, Arkolakis, Costinot and Rodriguez-Claire (2012) between 0.7% and 1.4%). A way to let a model with local labor markets collapse to one with a unique frictionless labor market is to assume that commuting can occur costlessly between any two locations, i.e. J (r) = R 8r and dij = 18i; j: in such a case, the local labor supply to any j would be much more elastic than it is in a world with (limited) commuting, and hence more of the adjustment can occur on labor quantities, and less on wages. Figure 2 shows that residents in all locations bene…t in real terms, and these gains range from 2.76% to 3.9% (about 34% of the mean gain)57 . One may wonder whether the lack of predictability of real wages based on exposure 57
Note that data at PUMA level allows the model to highlight within-state heterogeneity in the impact of trade.
40
measures shown above is a consequence of the particular example chosen (for example, the relatively small scale of the change in frictions) or is a more robust result. To investigate this aspect, I repeat the exercise above relating changes in wages to exposure to trade. To allow for separate impacts of trade in sectors where the United States have (or have not) an overall comparative advantage, I divide manufacturing sectors in the United States according to whether they will be in surplus or in de…cit after trade, and measure the exposure to liberalization with the manufacturing share of em(exp) (imp) ployment in these two groups of sectors, empr and empr . I then regress changes in nominal wages of workers and residents, and real wages of residents, on these two , the coe¢ cient associated and (imp) measures of exposures. Table 14 reports (exp) r r (exp) (imp) to empr and empr , respectively. Again, a larger exposure in sectors where the United States have a comparative advantage tends to raise nominal wages of workers, and to a lesser extent of residents (and vice-versa, larger exposure to sectors where the United States will be a net importer tends to lower them); however, the association becomes much ‡atter and with basically zero predictive power when it comes to real wages.58 Also, note that while locations more active in comparative-disadvantage sectors may su¤er in relative terms from trade, everybody gains, i.e., the level e¤ect is positive. Empirical exercises which do not capture such a level e¤ect provide only limited information on the real wage impact of trade. Overall, these results suggest that the choice of establishment-based data (i.e., job-location outcomes) vs. household or individual-level data (i.e., residence based outcomes) and, more importantly, the possibility of measuring or constructing real wages may signi…cantly impact the our assessment of the welfare consequences of trade across areas of a country.59
58
In table A10 in the Appendix, I use the inverse of the 2005 level of trade costs to proxy for the extent of liberalization in each sector: if in a sector s there was no liberalization, (s) = 1, and d (s) = 0, while as s becomes progressively freer of frictions, d (s) ! 1. These changes are weighted with the share of each sector in location r’s manufacturing employment, separately for surplus and de…cit sectors. The signi…cance of many coe¢ cients worsens, and the overall the predictive power follows the same pattern indicated in Table 14. 59 For example, Topalova, 2010, studying poverty changes in India, can only partially control for change in prices, as the poverty line is adjusted over time at state level, while exposure is measured at district level. Autor, Dorn and Hanson, 2013 use changes in average wages of residents across U.S. commuting zones but cannot control for changes in residence-speci…c price indices because of data limitations. Note that the empirical literature also di¤ers in the nature of data used to compute exposure: Topalova, 2010 uses Indian census, i.e. a residence-based measure, while Autor, Dorn and Hanson, 2013 use job location-based measures to compute industrial composition at their respective geographical unit of analysis.
41
Table 14: Exposure to international trade and local wages A: Unweighted (exp) r (imp) r
const R2 N
d ln wr
d ln w ~r
d ln(w ~r =pr )
0.063***
0.051***
0.002*
(0.003)
(0.003)
(0.001)
-0.079***
-0.064***
-0.002**
(0.003)
(0.003)
(0.001)
0.150***
0.150***
0.033***
(0.000)
(0.000)
(0.000)
0.67 1,230
0.57 1,230
0.01 1,230
B: Weighted by empl. in mfg d ln wr (exp) r (imp) r
const R2 N
d ln w ~r
d ln(w ~r =pr )
0.049***
0.040***
0.002**
(0.002)
(0.002)
(0.001)
-0.065***
-0.053***
-0.003***
(0.003)
(0.003)
(0.001)
0.150***
0.150***
0.033***
(0.000)
(0.000)
(0.000)
0.66 1,230
0.56 1,230
C: Weighted by overall empl. (exp) r (imp) r
const R2
0.03 1,230
N
d ln wr
d ln w ~r
d ln(w ~r =pr )
0.055***
0.045***
0.002***
(0.002)
(0.002)
(0.001)
-0.072***
-0.059***
-0.003***
(0.003)
(0.003)
(0.001)
0.150***
0.150***
0.033***
(0.000)
(0.000)
(0.000)
0.65 1,230
0.55 1,230
0.02 1,230
emp(exp)+ This table shows 3 panels of OLS estimates of equations of the form d ln yr = const+ (exp) r (imp) emp(imp), where each panel weighs observations as indicated. emp(exp) and emp(imp) are r the initial share of manufacturing employment of sectors where U.S. will be net exporter and net importer, respectively, in location r. In each panel, the …rst column shows results for yr = wr , the nominal wage of workers in r, the second for yr = w ~r , the average nominal wage of residents in r, and the third for yr = w ~r =pr , the average real wage of residents in r. * p < 0.1; ** p < 0.05; *** p < 0.01. Robust standard errors in parentheses.
8
Conclusions and limitations
The welfare consequences of international integration across areas of a country often occupies a central place in the public debate. A recent, yet substantial, literature has empirically documented the existence of heterogeneous e¤ects of trade in space. This contribution hopes to further our understanding of the e¤ect on real wages by showing how one can, …rst, take into account equilibrium interactions among local labor markets, and second, supplement the lack of measured price indices (in ex-post assessments) or their sheer unavailability (in the evaluation of new policy proposals). It also provides a framework within which to interpret di¤erence-in-di¤erence empirical exercises for the evaluation of episodes of international integration across locations. Importantly, a number of potentially relevant aspects have been left out of the analysis. Input-output linkages and an explicit intermediate good sector may mag-
42
nify the impact of trade and the interdependencies across locations. Di¤erences in skills may be re‡ected in di¤erent opportunity costs of time and hence heterogeneous sensitivity of commuting ‡ows to relative wages, and produce new results on the interaction between geography and skill di¤erences in shaping the impact of trade on inequality. Embedding this framework in an explicitly dynamic model will shed light on important di¤erences between short and long run behavior across areas. Internal labor mobility would add an additional transmission mechanism, through which local labor supply increases when geographic wage di¤erentials cannot be supported given sunk costs of moving. This paper illustrates how much shocks can propagate in absence of these additional channels. A reader should interpret these empirical results just as a …rst step towards a more complete understanding of the geographic incidence of trade (and other) shocks, which I hope will be easier to analyze in light of this contribution.
References [1] Allen, Treb, and Costas Arkolakis, 2014. "Trade and the Topography of the Spatial Economy", Quarterly Journal of Economics, February. [2] Ahlfeldt, Gabriel M., Stephen J. Redding, Daniel M. Sturm, Nikolaus Wolf, 2012. "The Economics of Density: Evidence from the Berlin Wall", CEP Discussion Paper N. 1154, June 2012. [3] Artuç, Erhan & Shubham Chaudhuri & John McLaren, 2010. "Trade Shocks and Labor Adjustment: A Structural Empirical Approach," American Economic Review, American Economic Association, vol. 100(3), pages 1008-45, June. [4] Artuç, Erhan & John McLaren, 2012. "Trade Policy and Wage Inequality: A Structural Analysis with Occupational and Sectoral Mobility," NBER Working Papers 18503, National Bureau of Economic Research [5] Autor, David H., David Dorn and Gordon H. Hanson, 2013. "The China Syndrome: Local Labor Market E¤ects of Import Competition in the United States," American Economic Review, American Economic Association, vol. 103(6), pages 2121-68, October. [6] Becker, Randy, Wayne Gray, Jordan Marvakov, NBER-CES Manufacturing Industry Database, Updated Data 1958-2009, June 2013. [7] Blanchard, Olivier J. & Lawrence F. Katz, 1992. "Regional Evolutions," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 23(1), pages 1-76. [8] Borjas, George J., and Valerie A. Ramey, 1995. “Foreign Competition, Market Power, and Wage Inequality.”Quarterly Journal of Economics, 110(4), 1075-1110
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[9] Caliendo, Lorenzo, and Fernando Parro, forthcoming. "Estimates of trade and welfare e¤ects of NAFTA", Review of Economic Studies. [10] Caliendo, Lorenzo, Fernando Parro, Esteban Rossi-Hansberg Pierre-Daniel Sarte, 2014: "The Impact of Regional and Sectoral Productivity Changes on the U.S. Economy", NBER working paper w20618, May 2014. [11] Cosar, Kerem, 2013. "Adjusting to Trade Liberalization: Reallocation and Labor Market Policies", working paper, January. [12] Chiquiar, Daniel, 2008. “Globalization, Regional Wage Di¤erentials, and the Stolper-Samuelson Theorem: Evidence from Mexico.” Journal of International Economics, 74 (1), 70-93. [13] Cosar, Kerem and Pablo D. Fajgelbaum, 2013: "Internal Geography, International Trade, and Regional Specialization", working paper, November. [14] Costinot, Arnaud, Donaldson, Dave, and Ivana Komunjer 2012. "What goods do countries trade? A Quantitative Exploration of Ricardo’s Ideas", Review of Economic Studies (2012) 79, 581–608. [15] Dekle, Robert & Jonathan Eaton & Samuel Kortum, 2008. "Global Rebalancing with Gravity: Measuring the Burden of Adjustment," IMF Sta¤ Papers, Palgrave Macmillan, vol. 55(3), pages 511-540, July. [16] di Giovanni, Julian, Andrei A. Levchenko, Jing Zhang, 2013. "The Global Welfare Impact of China: Trade Integration and Technological Change", Working paper, May. [17] Dix-Carneiro, Rafael, 2014. "Trade Liberalization and Labor Market Dynamics", Econometrica, Volume 82 Issue 3. [18] Donaldson, Dave (forthcoming). "Railroads of the Raj: Estimating the Impact of Transportation Infrastructure", American Economic Review. [19] Donaldson, Dave and David Atkin, 2013. Who’s Getting Globalized? The Size and Nature of Intranational Trade Costs", working paper, June. [20] Donaldson, Dave, and Richard Hornback, 2013. "Railroads and American Economic Growth: a "Market Access" approach", NBER working paper w19213. [21] Glaeser, Edward L. & Joseph Gyourko, 2005. "Urban Decline and Durable Housing," Journal of Political Economy, University of Chicago Press, vol. 113(2), pages 345-375, April. [22] Hanson, Gordon, 2005. "Globalization, Labor Income, and Poverty in Mexico", NBER Working paper w11027, January. [23] Hasan, Rana, Devashish Mitra, Priya Ranjan, and Reshad N. Ahsan, 2012. "Trade liberalization and unemployment: Theory and evidence from India". Journal of Development Economics, Volume 97, Issue 2, March 2012, Pages 269– 280. [24] Hasan, Rana, Devashish Mitra, and Beyza Ural, 2006. Trade Liberalization, Labor-Market Institutions, and Poverty Reduction: Evidence from Indian States, India Policy Forum, 2006-07.
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[25] Hsieh, Chang-Tai and Ralph Ossa, 2011. "A Global View of Productivity Growth in China", NBER working paper w16778, September. [26] Kennan, John & James R. Walker, 2011. "The E¤ect of Expected Income on Individual Migration Decisions," Econometrica, Econometric Society, vol. 79(1), pages 211-251, 01. [27] Kovak, Brian K. 2013. "Regional E¤ects of Trade Reform: What Is the Correct Measure of Liberalization?" American Economic Review, 103(5): 1960-76. [28] Mas-Colell, Andreu, Michael D. Whinston and Jerry R. Green, "Microeconomic Theory", Oxford University Press, New York, Jun 15, 1995. [29] McCaig, Brian 2011. "Exporting out of poverty: Provincial poverty in Vietnam and U.S. market access," Journal of International Economics, Elsevier, vol. 85(1), pages 102-113, September. [30] McLaren, John, and Shushanik Hakobyan. 2010. “Looking for Local Labor Market E¤ects of NAFTA.”NBER Working Paper No. 16535, July. [31] Monte, Ferdinando, Steve Redding and Esteban Rossi-Hansberg, 2015. "Commuting, Migration, and Local Employment Elasticities", NBER Working Paper w21706. [32] Notowidigdo, Matthew J. 2013. “The Incidence of Local Labor Demand Shocks.” working paper, March. [33] Ossa, Ralph, 2012. "Why Trade Matters After All", NBER Working Paper 18113, May. [34] Ruggles, Steven, J. Trent Alexander, Katie Genadek, Ronald Goeken, Matthew B. Schroeder, and Matthew Sobek. Integrated Public Use Microdata Series: Version 5.0 [Machine-readable database]. Minneapolis: University of Minnesota, 2010. [35] Topalova, Petia. 2005. “Trade Liberalization, Poverty, and Inequality: Evidence from Indian Districts.”NBER Working Paper w11614. [36] Topalova, Petia. 2010. “Factor Immobility and Regional Impacts of Trade Liberalization: Evidence on Poverty from India.”American Economic Journal: Applied Economics, 22, 1-41. [37] Topel, Robert H, 1986. "Local Labor Markets," Journal of Political Economy, University of Chicago Press, vol. 94(3), pages S111-43, June.
45
The Local Incidence of Trade Shocks Ferdinando Monte March 17, 2016
Online Appendix A
Tables and Figures Table A1: Number of destinations by PUMA, Min p10 p25 p50 p75 p90 2000 16 33 43 61 100 173 2005 5 15 21 30 51 84 2006 6 15 20 31 52 88 2007 5 16 21 31 54 89 ALL 5 17 23 37 63 101
weighted by hours supplied Max Mean N 254 81.01 234.5 119 40.01 250.1 120 40.83 260.0 120 41.43 262.4 254 50.14 1,007.1
This table reports selected percentiles in the out-degree distribution of commuting patterns, i.e. the number of PUMAs of work chosen by at least one worker from any PUMA of residence. The …rst row uses Census 2000, the following three ACS in the reported years, and the last aggregates all years. Each PUMA of residence receives a weight proportional to the yearly hours of labor supplied by all residents. The last column reports total hours worked in a year, in billions.
2000 2005 2006 2007 ALL
Table Min 36.81 40.19 41.94 44.63 36.81
A2: Total hours of work supplied to a PUMA (in million) p10 p25 p50 p75 p90 Max Mean N 69.49 84.33 110.36 165.11 296.30 6,230.56 192.32 1,230 73.35 86.63 116.46 173.05 313.90 7,062.51 204.13 1,230 75.43 92.03 119.96 179.74 330.89 7,395.70 212.18 1,230 73.81 90.63 120.47 179.84 332.39 7,438.68 214.14 1,230 72.65 88.14 116.83 174.94 316.28 7,438.68 205.69 4,920
This table reports selected percentiles in the distribution of the hours of work supplied to a PUMA. All values are in millions of hours. The …rst row uses Census 2000, the following three ACS in the reported years, and the last aggregates all years.
46
Table A3: Average hourly income by Min p10 p25 p50 p75 2000 13.59 15.94 17.05 19.10 21.95 2005 12.45 15.68 16.93 19.10 22.11 2006 13.14 15.51 16.79 18.95 21.71 2007 13.39 15.83 17.19 19.36 22.05 ALL 12.45 15.72 16.99 19.11 21.95
PUMA p90 25.01 25.68 25.12 25.59 25.38
of work Max 38.27 48.05 38.88 44.53 48.05
(dollars) Mean N 19.89 1,230 20.02 1,230 19.76 1,230 20.12 1,230 19.95 4,920
This table reports selected percentiles in the distribution of the hourly income of hours of work supplied to a PUMA. Hourly income in a PUMA is computed as the total income received by all employed people in a PUMA (pre-tax wage and salary income, plus pre-tax self-employment income from a business, professional practice, or farm, if present), divided by the total hours supplied to the same PUMA. All values are 2007 dollars. The …rst row uses Census 2000, the following three ACS in the reported years, and the last aggregates all years.
Table A4: The manufacturing sector across PUMAs of Panel A: Number of active manufacturing sectors Min p10 p25 p50 p75 p90 Max Mean 2000 12 17 18 19 20 21 21 19.20 2005 2 11 13 15 17 19 21 14.76 2006 5 10 13 15 17 19 21 14.82 2007 3 11 13 15 17 19 21 14.91 ALL 2 11 14 16 19 20 21 15.92
2000 2005 2006 2007 ALL
Panel Min 0.02 0.01 0.01 0.01 0.01
B: Share of p10 p25 0.07 0.10 0.06 0.09 0.05 0.09 0.05 0.08 0.06 0.09
hours p50 0.16 0.14 0.14 0.13 0.14
employed in p75 p90 0.23 0.29 0.20 0.26 0.20 0.25 0.19 0.25 0.21 0.26
work
manufacturing Max Mean 0.51 0.17 0.51 0.15 0.49 0.15 0.49 0.14 0.51 0.15
N 1,230 1,230 1,230 1,230 4,920 N 1,230 1,230 1,230 1,230 4,920
This table reports selected percentiles in the distribution of the manufacturing sector (NAICS 311339) across PUMAs of work. Panel A reports the number of di¤erent 3-digit NAICS sectors active in manufacturing across PUMAs. Panel B reports the share of hours employed in manufacturing over the total employment in a PUMA. In each Panel, the …rst row uses Census 2000, the following three ACS in the reported years, and the last aggregates all years.
47
Table A5: Concentration of manufacturing activity across sectors Panel A: Number of locations where a sector is active Min p10 p25 p50 p75 p90 Max Mean N 2000 0.53 0.76 0.90 0.98 0.99 1.00 1.00 0.91 21 2005 0.20 0.37 0.49 0.79 0.91 0.93 0.95 0.70 21 2006 0.20 0.37 0.47 0.80 0.89 0.93 0.97 0.71 21 2007 0.20 0.37 0.47 0.80 0.91 0.94 0.96 0.71 21 Panel B: Share Min 2000 0.28 2005 0.29 2006 0.30 2007 0.31
of employment of p10 p25 p50 0.29 0.32 0.39 0.31 0.33 0.40 0.31 0.31 0.40 0.31 0.33 0.41
a sector in the top 5% of PUMAs p75 p90 Max Mean N 0.55 0.56 0.65 0.42 21 0.57 0.66 0.67 0.45 21 0.58 0.65 0.69 0.44 21 0.56 0.65 0.68 0.44 21
This table reports selected percentiles in the distribution of the concentration of di¤erent manufacturing sectors (NAICS 311-339). Panel A shows the fraction of di¤erent PUMAs (out of 1,230) where a given sector has positive employment. Panel B refers to the share of a sector’s employment accounted for by the largest 5% of PUMAs in terms of employment in the sector (62 locations). In each Panel, the …rst row uses Census 2000, and the following three ACS in the reported years.
48
49
Naics Name Share Mfg. Avg. Wage Fr. Zeros CIF/FOB Imp. Pen. 311 Food Mfg. 0.08 17.71 0.05 0.09 1.09 0.06 312 Beverage and Tobacco Mfg. 0.01 24.43 0.42 0.02 1.06 0.10 313 Textile Mills 0.01 17.12 0.50 0.01 1.12 0.19 314 Textile Product Mills 0.01 15.53 0.45 0.01 1.13 0.29 315 Apparel Mfg. 0.02 16.15 0.38 0.02 1.16 0.70 316 Leather and Allied Products Mfg. 0.00 18.19 0.69 0.01 1.16 0.85 321 Wood Product Mfg. 0.03 17.07 0.15 0.02 1.07 0.18 322 Paper Mfg. 0.03 22.74 0.23 0.03 1.05 0.13 323 Printing and Related Support Activities 0.05 20.86 0.12 0.02 1.05 0.05 324 Petroleum and Coal Products Mfg. 0.01 31.49 0.57 0.09 1.05 0.16 325 Chemical Mfg. 0.08 29.95 0.07 0.11 1.04 0.21 326 Plastics and Rubber Products Mfg. 0.04 19.49 0.14 0.04 1.09 0.13 327 Nonmetallic Mineral Product Mfg. 0.03 19.60 0.11 0.02 1.14 0.16 331 Primary Metal Mfg. 0.04 21.52 0.20 0.04 1.05 0.28 332 Fabricated Metal Product Mfg. 0.09 19.82 0.03 0.06 1.06 0.13 333 Machinery Mfg. 0.08 22.62 0.05 0.06 1.04 0.34 334 Computer and Electronic Product Mfg. 0.10 31.13 0.14 0.11 1.02 0.50 335 Electrical Equipment, Appliance, and Component Mfg. 0.03 21.73 0.21 0.03 1.06 0.37 336 Transportation Equipment Mfg. 0.15 25.43 0.06 0.15 1.03 0.32 337 Furniture and Related Product Mfg. 0.04 16.89 0.16 0.02 1.11 0.24 339 Miscellaneous Mfg. 0.07 22.54 0.04 0.04 1.05 0.41 This table reports selected statistics on each 3-digit naics manufacturing sectors. Share Mfg is the share of hours of the sector in manufacturing, Avg. Wage is the average hourly wage in 2005 USD, Fr. Zeros is the fraction of PUMAs (out of 1,230) with zero employment in the sector, is the average expenditure share of U.S. in the sector as a fraction of total expenditure on manufactures, CIF/FOB is the CIF/FoB ratio for the sector, and Imp. Pen. is the rest of the worlds’share of U.S. expenditure in the sector. All numbers are the average of the years 2000, 2005 and 2006 data points: in these years all statistics could be computed.
Table A6: Selected statistics on manufacturing sectors
Table A7: GMM estimation of parameters of job location choice All distances Truncated distances Only 2000 Only 2005-07 All years Only 2000 Only 2005-07 All years 0
1
2
1
2
3
0
N
3.44***
4.46***
4.43***
5.38
4.99
4.03
(0.89)
(1.29)
(1.03)
(4.42)
(3.98)
(2.96)
-0.44***
-0.41***
-0.43***
-0.78***
-0.73**
-0.68**
(0.08)
(0.07)
(0.07)
(0.26)
(0.30)
(0.27)
0.23***
0.22***
0.22***
0.43***
0.41***
0.39***
(0.05)
(0.04)
(0.04)
(0.13)
(0.15)
(0.14)
-0.98***
-2.00*
-1.48**
-0.16
-0.35
-0.34
(0.32)
(1.03)
(0.59)
(0.22)
(0.38)
(0.33)
0.17***
0.26**
0.23***
0.03
0.03
0.04
(0.05)
(0.13)
(0.09)
(0.03)
(0.04)
(0.04)
-0.12***
-0.20*
-0.16**
-0.02
-0.03
-0.03
(0.04)
(0.10)
(0.07)
(0.02)
(0.03)
(0.03)
4.57***
6.23**
5.58***
1.67**
1.79*
1.86*
(1.00)
(2.70)
(1.76)
(0.68)
(1.05)
(0.96)
64,654
96,912
161,566
32,397
65,078
97,475
This table shows GMM estimates for eq. 16. Each column reports the results of a particular GMM estimate: columns di¤er only according to the sample used. The …rst three columns use all observed bilateral commuting ‡ows; the last three only bilateral commuting ‡ows between PUMAs whose centroids are less than 136.4 miles away from each other (i.e., exclude the top 1% of commuters). Within each set of three columns, the …rst uses only commuting data from then Census 2000, the second only data from ACS 2005-2007, and the third all data together. * p < 0.1; ** p < 0.05; *** p < 0.01. Standard errors in parentheses.
50
Table A8: GMM estimates of eq. 16, with time dummies for the constant All distances Truncated distances Only 2005-07 All years Only 2005-07 All years 0
1
2
1
2
3
0
1
2
N
4.45***
3.71***
4.99
4.04
(1.29)
(0.82)
(3.98)
(2.93)
-0.41***
-0.42***
-0.73**
-0.68**
(0.07)
(0.07)
(0.30)
(0.27)
0.22***
0.22***
0.41***
0.38***
(0.04)
(0.04)
(0.15)
(0.14)
-1.99*
-1.35***
-0.35
-0.34
(1.03)
(0.50)
(0.38)
(0.33)
0.26**
0.20***
0.03
0.04
(0.13)
(0.07)
(0.04)
(0.04)
-0.20*
-0.15***
-0.03
-0.03
(0.10)
(0.06)
(0.03)
(0.03)
6.19**
4.62***
1.78*
1.73*
(2.68)
(1.30)
(1.05)
(0.90)
0.04
0.03
0.01
0.01
(0.03)
(0.02)
(0.01)
(0.01)
0.05
0.04*
0.01
0.01
(0.03)
(0.02)
(0.01)
(0.01)
96,912
161,566
65,078
97,475
This table shows GMM estimates for eq. 16, adding year dummies to the constant. Each column reports the results of a particular GMM estimate: columns di¤er only according to the sample used. The …rst three columns use all observed bilateral commuting ‡ows; the last three only bilateral commuting ‡ows between PUMAs whose centroids are less than 137 miles away from each other (i.e., exclude the top 1% of commuters). Within each set of three columns, the …rst uses only commuting data from then Census 2000, the second only data from ACS 2005-2007, and the third all data together. * p < 0.1; ** p < 0.05; *** p < 0.01. Standard errors in parentheses.
51
Table A9: Coe¢ cient
in estimation of eq. 17 and eq. 18 with year F.E. Dep. var: wage bill Dep. var: tot. hours N +1 N
OLS
-0.61***
78,292
(0.12)
IV: only local
7.68***
78,292
(1.76)
IV: local and 50 miles
78,292
8.42***
78,292
(1.57)
4.32***
70,271
(1.36)
IV: local and 200 miles
-0.08 (0.10)
4.97***
70,271
(1.19)
3.24** (1.46)
78,292
3.87***
78,292
(1.30)
This table shows estimates of equation 17 (left column, reporting ) and equation 18 (right column, reporting + 1); it di¤ers from Table 9 in the fact that it adds year …xed e¤ects. The …rst row shows results for an OLS regression of the dependent variable (total wage bill or total hours in location j and sector s) on sector, locations, year and sector-year …xed e¤ects. The second row show IV estimates of the same equations, where the instrument is the total population 16 y/o and older and labor force living in j. The third and fourth rows add population 16 y/o and older and labor force in PUMAs whose centroid is within 50 miles, or within 200 miles, from the centroid of j, respectively. * p < 0.1; ** p < 0.05; *** p < 0.01. Standard errors in parentheses.
52
Table A10: Exposure to international trade and local wages: alternative measure of exposure Panel A: Unweighted (exp) r (imp) r
const
d ln wr
d ln w~r
-0.033
-0.020
0.006
(0.022)
(0.021)
(0.006)
-0.057***
-0.039*
0.005
(0.022)
(0.021)
(0.006)
0.233***
0.204***
0.022*
(0.042)
(0.040)
(0.012)
R2 0.61 N 1,230 Panel B: Weighted by empl. in mfg (exp) r (imp) r
const
d ln w~r
d ln(w~r =pr )
0.023
0.023
0.005
(0.026)
(0.025)
(0.009)
-0.007
-0.002
0.004
(0.025)
(0.025)
(0.008)
(0.048) 2
R N
0.50 0.01 1,230 1,230 Panel C: Weighted by overall empl.
d ln wr
0.132*** 0.127*** 0.68 1,230
(0.047)
0.57 1,230
d ln(w~r =pr )
0.024
(exp) r (imp) r
const
(0.016)
0.02 1,230
2
R N
d ln wr
d ln w~r
d ln(w~r =pr )
0.016
0.021
0.008
(0.022)
(0.021)
(0.006)
-0.009
0.000
0.008
(0.022)
(0.020)
(0.006)
0.141*** 0.128***
0.018
(0.041)
(0.039)
(0.011)
0.61 1,230
0.50 1,230
0.01 1,230
(exp) This table shows 3 panels of OLS estimates of equations of the form d ln yr = const + (exp) + r r P (imp) (imp) (exp ) (s) (s) , where each panel weighs observations as indicated, = d r r r s2SM (j);s2exp P (s0 ) (s) P (im p ) (s) (s) (s) and r , where = Hr = s0 2SM (j) Hr : In these expressions, s 2exp if = s2SM (j) d s2im p
s is a sector where U.S. is a net exporter in the current-tari¤s equilibrium (and viceversa for s 2imp), and d (s) = 1= (s) , the reciprocal of the average level of trade costs as reported in table A6. In each panel, the …rst column shows results for yr = wr , the nominal wage of workers in r, the second for yr = w ~r , the average nominal wage of residents in r, and the third for yr = w ~r =pr , the average real wage of residents in r. * p < 0.1; ** p < 0.05; *** p < 0.01. Robust standard errors in parentheses.
53
Fraction of hours commuting outside the residence
Figure A1: Commuting and distance 2000
2005
2006
2007
1 .1 .01 .001 .0001 .00001
1 .1 .01 .001 .0001 .00001
2
10
50
200
800
3200
2
10
50
200
800
3200
Distance in miles, log scale
For each year, this …gure plots the share of hours commuting from any PUMA of residence r to all PUMAs of work j (excluding r itself) out of the total hours of work supplied by residents in r, againts distance between r and j. The distance between two PUMAs is computed as the distance between their centroids using Haversine’s formula.
Figure A2: Elasticity of labor supply to a PUMA to its own wage Worcester Springfield
Boston
Providence
Hartford Waterbury New Haven Bridgeport
0.00 - 0.86
Stamford
0.87 - 1.62 1.63 - 2.44
Paterson
2.45 - 3.57
Newark
3.58 - 5.33
Elizabeth
Yonkers
New York
This Figure shows the elasticity "(L(j); wj ) (eq. (8)) over the U.S. territory (left panel) and zooming on a portion of the East Coast (right panel). Elasticities are computed using observed data on commuting ‡ows in 2005 and estimates of r from the restricted sample reported in table 8.
54
.05
.1
model
.15
.2
Figure A3: Simulated and measured data across PUMAs
10
20
30 data - 2005 USD
40
50
Correlation: .88
This …gure shows a scatterplot of the hourly income across PUMAs in 2005 and the equilibrium wages in the simulated model using parameters estimated from the data. Wages in the data are in 2007 dollars.
Figure A4: Components of the e¤ects of trade liberalization in CEP no empl. in CEP
with empl. in CEP
.06 .04 0
0
10
20
30
0
% contribution of direct effect
50
100
0
50
100
% contribution from connected labor markets
with empl. in CEP
no empl. in CEP
with empl. in CEP
.05 0
0
.05
fraction of PUMAs
.1
.1
no empl. in CEP
fraction of PUMAs
.02
fraction of PUMAs
.1 .05 0
fraction of PUMAs
.08
with empl. in CEP
0
10
20
30
0
10
20
30
0
% contribution from unconnected labor markets
20
40
60
0
20
40
60
% contribution from trade rebalancing
This …gure shows the contribution of di¤erent terms in Prop. 3 to the total impact of a liberalization in CEP, across PUMAs. The label along the x-axis of each panel reports the term to which the distribution is referring. For the direct e¤ect only PUMAs active in CEP are considered; for the other three e¤ects, the histograms are broken down according to whehter PUMAs have a positive empolyment in CEP or not.
55
Figure A5: Overpredictions in a No-Commuting Model 1
0
.1
Fraction
.2
.3
0
.8
1
1.2
1.4 .8
1
1.2
1.4
% DWage in j (no commuting) / % DWage in j (with commuting)
This …gure shows the distribution of the overprediction of changes in wages generated by a model with no commuting, if the true data-generating process actually has commuting ‡ows; in particular, the overprediction for location j is de…ned as the change in wage in the location in the no-commuting model divided by the change in the with-commuting model. The left and right panel refer to locations not active and active in CEP, respectively.
.15
% change in wage - no commuting .2 .25 .3
.35
Figure A6: Wage changes in the with-commuting and no-commuting model
.15
.2 .25 .3 % change in wage paid - with commuting with empl. in CEP
.35
no empl. in CEP
This …gure shows a scatterplot of the percentage change in wages paid to workers in a PUMA implied by the true, with-commuting model, vs. the percentage change in wages paid to workers in the same PUMA generated by a no-commuting model, when trade frictions in CEP are eliminated. The scatterplot separates locations where CEP is active from those where CEP is not active. The black, dashed line is a 45 degrees line.
56
B B.1
Proofs and Supporting Algebra Elasticities of labor demand
Labor demand in j is given by 2 1 4 X D (j) = wj
(s) (s) X j
+
(s) (s) X j
+
(s)
s2SM (j)
P
3
w ~j Hj 5
with w~r = j 0 2J (r) mr (j 0 ) wj 0 : Note that, using (7), @w ~r @wj 0
=
wj 0 @ w ~r w ~r @wj 0
=
X @mrj wj = @wj 0
j2J (r)
X
j2J (r)nj 0
X
=
1
j2J (r)nj 0
@mrj @mrj 0 wj + mrj 0 + wj 0 =) @wj 0 @wj 0
mrj wj wj 0 @mrj wj 0 mrj 0 wj 0 @mrj 0 mrj 0 wj 0 + + = w ~r mrj @wj 0 w ~r mrj 0 @wj 0 w ~r wj 0 mrj 0 1 1 mrj wj mrj + + (1 w ~r w ~r r r
j2J (r)nj 0
=
X
X mrj wj 1 mrj 0 + 1 + w ~r r
r j2J (r)
mrj 0 )
mrj 0 wj 0 = w ~r
mrj 0 wj 0 w ~r
The response to a change in wj is @D (j) @wj
1 1 4 X D (j) w + j wj wj2
=
s2SM (j)
~j (s) @ w
+ wj @D (j) D (j) @wj
2
@wj =
(s)
wj @ j (s) @w j j
=
1+
@wj
@X (s) X+ @wj
(s) (s) j
+
@
(s) j
(s)
@wj
Hj =)
X
(s)
X
wj @ j (s) (s) wj @X X+ j (s) @w X @wj j j s2SM (j) ! wj @ w ~j (s) 1 (s) (s) + w ~ j Hj j X wj D (j) w ~j @wj
1 1+ wj D (j) +
(s) j
@
1
(s) j
s2SM (j)
wj @ w ~j + w ~j @wj
(s) j
57
+
wj @X X @wj
(s) j
1
(s) (s) j X
(s) j
+
(s) j
+
X
!
(s) (s) (s) (s) (s) X = (w D (j)) ; and (s) (s) w where (s) X= (wj D (j)), j ~j Hj = (wj D (j)) : j j j j To compute the response of labor demand in j to a change in a wage in wj 0 with j 6= j 0 and j 0 2 J (j), we have
@D (j) @wj 0 wj 0 @D (j) D (j) @wj 0
=
0 1 @ X wj
(s)
X
s2SM (j)
=
1 1 wj D (j) +
@
(s) j
(s) j
+
@wj 0
(s)
X
wj 0 @ j + (s) @w 0 j
(s) (s) X j
(s)
(s)
X
1 @ w ~ j + (s) Hj A =) @wj 0 (s)
wj 0 @ j @X + (s) X @wj 0 @wj 0
(s) (s) wj 0 X j
j
s2SM (j)
~j 1 1 wj 0 @ w wj D (j) w ~j @wj 0
!
(s)
@ j (s) @X + @wj 0 @wj 0
(s) (s) j X
j
!
w ~j Hj
and since D (j) wj is in equilibrium the total labor payments to workers working in location j wj 0 @D (j) D (j) @wj 0
=
X
s2SM (j)
=
"
X
(s) j0
wj 0 @X + X @wj 0
(s) j0
+
s2SM (j)
X
=
(s) (s) X j
D (j) wj
wj 0 @X X @wj 0 (s) (s) j0 j
(s) j
+
s2SM (j)\SM (j 0 )
(s) j0
D (j) wj
(s) (s) j0 j
+
(s) (s) j0 j
+
+
(s) (s) X j
+
wj 0 @X X @wj 0
~j wj 0 @ w w ~j @wj 0 X
#
(s) j (s) j
wj 0 @ w ~j (s) w ~j Hj = w ~j @wj 0 D (j) wj
+ =
+
s2SM (j)
~j wj 0 @ w w ~j @wj 0
(s) j
(s) where the last equality follows from the fact that (s) j and j 0 are a function of wj 0 if 0 0 and only if s 2 S (j ). The last term disappears if j 62 J (j) as changes in wj 0 would not directly a¤ect the average wage in location j . The response to a change in the foreign wage is
@D (j) @w w @D (j) D (j) @w w @D (j) D (j) @w
=
1 wj
X
(s)
X
@
s2SM (j)
=
1 1 wj D (j)
=
X h
(s) j
@w
+
@w
@X (s) X + @w (s)
X
(s) (s) X j
(s)
+
(s)
+1
s2SM (j)
58
(s) (s) j
j
(s) j
i
!
=)
(s)
w @ j w @ j + (s) (s) @w @w j
s2SM (j) (s) j
(s) j
@
(s) (s) j X
w @X + X @w
(s) (s) j X
!
+
B.2
Existence and local uniqueness
As trade balance holds if and only if the RoW’s labor market is in equilibrium, it is su¢ cient to prove the Propositions with reference to an economy with R locations, where one is the foreign country’s local labor market: from the perspective of the theory, this market is simply one with no commuting ties to the Home economy and speci…c transportation costs. Proposition 1. An equilibrium vector w exists. Proof. Consider the excess demand system Zj (w1 ; :::; wR ) = Dj (w) Lj (w) = 2 0 X X 1 4 @ (s) (s) mrj 0 (w) wj 0 + = j wj s2SM (j) j 0 2J (r) X mrj (w) Hr r2J
1
(s) (s) w j
1
H A+
(s)
3
w ~j Hj 5 +
(j)
for j = 1; :::; R. Z is continuous as each Zj is given by sums and products of continuous functions. We have made the dependence on w explicit now. Labor supply is homogeneous of degree 0 (HD0) in wages, as mrj (w) is HD0. It is easy to show that labor demand is HD0 as well, since j (w) is also HD0 (hence, Z is HD0) and that Walras’law holds. Labor demand in each location j is always strictly positive, and has a lower bound P at zero. Labor supply in each location j has an upper bound in r2J 1 (j) Hr . Let k nP o J . maxj L (j; w) > L (j; w) > k , 8w 2 R++ r2J 1 (j) Hr . Hence, Zj (w) = D (j; w) Consider now a sequence fwgn ! w0 , where wj0 6= 0 and wj00 = 0 for some j 0 . De…ne J 0 R as the set of j 0 : wj00 = 0. Suppose …rst that J 0 has cardinality 1, i.e. there is only one j 0 such that wj 0 = 0: then (s) j 0 (w) ! 1 (for all s 2 SM (j)) and mrj 0 (w) ! 0; more(s) 0 over, for j 6= j , j (w) approach either zero (if s 2 SM (j)) or a constant (otherwise), P P and mrj (w) ! mrj w0 2 (0; 1]: Hence, national income r2R Hr j2J (r) mrj (w) wj approaches a positive constant, while Dj 0 (w) ! +1. Hence, the excess demand function Zj 0 (w) also approaches +1 since labor supply in any location is always bounded above by k. Suppose now J 0 has cardinality larger than one. If, as fwgn ! w0 ; there is only one j 0 which goes to zero faster than all the others, then we can apply to that j 0 the argument above. If a number n of them approach zero at the same speed (i.e., their ratio approaches 1), then the trade share approach either 1 (if only 59
one j 0 is approaching zero among those active in n), or a constant between zero and 1. Labor supply always approaches a positive constant; we can then conclude that Dj 0 (w) ! +1 for all those j 0 : Hence, properties (i)-(v) in Proposition 17.B.2 of Mas-Colell, Whinston and Green (1995) hold. An equilibrium where Z(w) = 0 then exists by proposition 17.C.1 of MasColell, Whinston and Green (1995). To prove Proposition 2 on local uniqueness, we …rst prove the following lemma. Lemma 4 Let dZH (w) =
h
i
@Zj @Hr r;j=1;:::J 1
be a matrix where the r; j
th element is the
derivative of the excess labor demand in location j with respect to the population resident in r, Hr , evaluated at the wage vector w. dZH (w) is generically invertible. Proof. Denote the r; j
th element of dZH (w) with frj (w). From the expression
J of the excess labor demand, fij (w) :R++ ! R and fij (w) 2 C 1 : The determinant J of dZH (w) is then a function a (w) : R++ ! R, and is also C 1 . We now show J . Note …rst J : a (w) = 0 has zero Lebesgue measure in R++ that the set w 2 R++ that to show this property, it is su¢ cient to show that for a …xed arbitrary vector w 1 [w2 ; ::::; wJ ], there is no open interval for w1 where a (w1 ; w 1 ) = 0 (i.e., there is no interval for w1 where a (w1 ; w 1 ) is ‡at and equal to zero) ; in this case, in fact, there would be at most a countable set of points where dZH (w) is not invertible, J 1 and this set would have measure zero. Fix then an arbitrary w 1 2 R++ , and consider the function a (w1 ; w 1 ), viewed as a function of one variable, w1 . Two cases are possible: either @ w1 2 R++ : a (w1 ; w 1 ) = 0, or 9 w1 2 R++ : a (w1 ; w 1 ) = 0. In the …rst case, the determinant is never zero, and hence dZH (w1 ; w 1 ) is invert0 J ible for all w0 2 R++ : w 1 = w 1 , w1 2 R++ . In the second case, the matrix is not invertible for at least some w1 ; for this case, we show that 9 > 0 such that 8w ~ 2 fw ~ 2 R++ : jw ~ w1 j < ; w ~ 6= w1 g, it is true that a (w; ~ w 1 ) 6= 0. Note in fact that the point (w1 ; w 1 ) can either be a critical point for a (w) or not. If it is not, then @a (w; ~ w 1 ) =@ wj ~ w=w 6= 0: hence a (w1 ; w 1 ) 6= 0 in a neighborhood of w1 . If it ~ 1 is a critical point, then @a (w; ~ w 1 ) =@ wj ~ w=w = 0; however, since a (w) 2 C 1 , it is ~ 1 generically a Morse function, i.e., all critical points are non-degenerate, and hence, @ 2 a (w; ~ w 1 ) =@ w ~ 2 jw=w 6= 0;a fortiori, there cannot be an interval where the second ~ 1 derivative is ‡at, i.e., where there is an interval of critical points around w1 . These J 1 arguments imply that for an arbitrary w 1 2 R++ , either the determinant of dZH (w) is non-zero for all w1 , or it is zero for a countable set of values for w1 ; in any case,
60
J they imply that w 2 R++ : a (w) = 0 has dimension at most J 1, and hence it has J . Hence, a (w ; w ) 6= 0 generically, and dZ (w) is zero Lebesgue measure in R++ 1 1 H generically invertible.
Proposition 2. Let w be an equilibrium; then this equilibrium is generically locally unique. Proof. Note that dZH (w ) is generically invertible by Lemma 4. Hence, we can move dZH (w ) in any desired direction in RJ
1
by setting dH vector appropriately. By the transversality theorem, since dZw;H has generically rank J 1, the (J 1) (J 1) matrix dZw also has rank J 1 generically. Hence, the equilibrium is generically locally unique. (See also proof of Proposition 17.D.4 in Mas-Colell, Whinston and Green (1995) for a similar argument).
B.3
Transmission of a change in V
Proposition 3. Let V be any exogenous parameter of the model. The elasticity of the wage paid in any location j to a shock to V is " (wj ; V ) =
" (D (j) ; V ) " (L (j) ; V ) + " (L (j) ; wj ) " (D (j) ; wj ) {z } | direct e¤ect
X
" (D (j) ; wj 0 ) " (L (j) ; wj 0 ) " (wj 0 ; V ) + " (L (j) ; wj ) " (D (j) ; wj ) 0 2 j 2J (j)nfjg | {z }
+
indirect e¤ect from connected labor markets
X
" (D (j) ; wj 0 ) " (wj 0 ; V ) + " (L (j) ; wj ) " (D (j) ; wj ) j 0 2RnJ 2 (j) | {z }
+
indirect e¤ect from unconnected labor markets
" (D (j) ; w ) + " (w ; V ) " (L (j) ; wj ) " (D (j) ; wj ) {z } | indirect e¤ect from trade balance
for a wage in a domestic economy, and " (w ; V ) =
" (N X; V ) " (N X; w ) | {z } direct e¤ect
61
X " (N X; wj ) " (wj ; V ) " (N X; w ) j2R | {z } indirect e¤ect
in the foreign economy, where " (N X; ) is the elasticity of exports to a variable less the elasticity of imports to the same variable. Proof. The total di¤erential of the labor supply with respect to the wages in the
whole economy only involves wages in the local labor market of j , J 2 (j): @L (j) @L (j) dwj + dV + @V @wj
X
j 0 2J 2 (j)nfjg
@L (j) dwj 0 @wj 0
Labor demand depends instead on the wages of the whole economy; its total di¤erential is @D (j) @D (j) dwj + dV + @V @wj
X
j 0 2Rnfjg
@D (j) @D (j) dwj 0 + dw @wj 0 @w
Equating these two terms, collecting those referring to market j , and dividing through dV , @L (j) @L (j) dV + dwj + @V @wj
X
j 0 2J 2 (j)nfjg
@L (j) dwj 0 = @wj 0
@D (j) @D (j) dV + dwj + @V @wj +
@L (j) dwj @wj dV
@D (j) dwj @wj dV
=
@D (j) @V +
X
@L (j) + @V
j 0 2RnJ 2 (j)
@D (j) dw @w
X
j 0 2J 2 (j)nfjg
@D (j) @wj 0
@L (j) @wj 0
X
j 0 2Rnfjg
@D (j) dwj 0 @wj 0
dwj 0 + dV
@D (j) dwj 0 @D (j) dw + @wj 0 dV @w dV
Multiplying both sides by V =L (j), and recalling that in equilibrium L (j) = D (j), we convert these terms into elasticities, and then divide through by " (L (j) ; wj ) " (D (j) ; wj ), to get V @L (j) V @D (j) (" (L (j) ; wj ) " (D (j) ; wj )) " (wj ; V ) = + D (j) @V L (j) @V X + (" (D (j) ; wj 0 ) " (L (j) ; wj 0 )) " wj0 ; V + j 0 2J 2 (j)nfjg
+
X
" (D (j) ; wj 0 ) " (wj 0 ; V ) + " (D (j) ; w ) " (w ; V )
j 0 2RnJ 2 (j)
62
and hence " (wj ; V ) =
" (D (j) ; V ) " (L (j) ; wj ) +
X
j 0 2RnJ 2 (j)
" (L (j) ; V ) + " (D (j) ; wj )
X
j 0 2J 2 (j)nfjg
" (D (j) ; wj 0 ) " (L (j) ; wj )
" (L (j) ; wj 0 ) " wj0 ; V " (D (j) ; wj )
" (D (j) ; wj 0 ) " (wj 0 ; V ) + " (D (j) ; w ) " (w ; V ) (" (L (j) ; wj ) " (D (j) ; wj ))
The elasticity of w to changes in V is determined by the trade balance: X
(s) (s)
X=
X
X
(s) (s) X j0
j 0 2R s2SM (j 0 )
s2SM
Denote with imp and exp total imports and total exports of the economy. The total di¤erential of the trade balance with respect to all the wages and V is then X
j2R
@imp dwj @wj
+
X @exp @imp @imp @exp @exp dV = dV dw + dwj + dw + @w @V @wj @w @V j2R
Oh the left-hand side, the …rst term gives the change in total imports as wages anywhere in the home economy change. The second term gives the change in total imports as the foreign wage increases (and hence it is always negative). The third term is the change in imports as a consequence of the change in V . The right-hand side contains analogous terms for exports. Grouping terms, dividing through by dV and expressing in terms of elasticities, exp
w @exp exp @w
w @imp V dw imp @w w dV
V @exp V @imp + exp @V imp @V X wj @exp wj @imp V dwj exp exp @wj imp @wj wj dV
=
exp
j2R
where the last row uses the fact that in equilibrium, imports and exports are the same. Hence, " (w ; V ) =
" (N X; V ) " (N X; w )
X " (N X; wj ) " (wj ; V ) " (N X; w )
j2R
where " (N X; ) denotes the elasticity of exports to a variable less the elasticity of imports to the same variable.
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B.4
Centrality
The analysis in proposition 3 expresses the elasticity of the wj to a change in parameter V as a function of the elasticity of all the other wages, plus a direct e¤ect, and can be written in compact form as " (w; V ) =
+A
" (w; V )
where " (w; V ) is an (R + 1) 1 vector of elasticities with j th element " (wj ; V ) (and the elasticity of w in the last row), is an (R + 1) 1 vector of direct e¤ects, A is a conformable square matrix containing the coe¢ cients of all the indirect e¤ects, and all terms are evaluated at the equilibrium wages. Note that this relation implies, " (w; V ) = [I
A]
1
which is related to eigenvector centrality in network theory. In our economy, a location j has high centrality if its equilibrium elasticity is large: in this case, in fact, anything happening to the wage in j has large consequences for all other locations when appearing on the right-hand sides of eq. (14) or (15). Locations with an elasticity close to zero act as "shock absorber", i.e. would not let it propagate to other connected and unconnected labor markets.
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